What is the exact value of sin 60

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Concept wise Trignometric ratios of Specific Angles - Evaluating Tired of ads? What is value of sin, cos, tan at 0, 30, 45, 60 & 90 degree? Last updated at May 29, 2023 by Teachoo What is value of sin …Explanation: For sin 135 degrees, the angle 135° lies between 90° and 180° (Second Quadrant ). Since sine function is positive in the second quadrant, thus sin 135° value = 1/√2 or 0.7071067. . . Since the sine function is a periodic function, we can represent sin 135° as, sin 135 degrees = sin (135° + n × 360°), n ∈ Z.Increased Offer! Hilton No Annual Fee 70K + Free Night Cert Offer! Hilton Grand Vacations has a new timeshare offer. You can get a three night stay and 50,000 Hilton Honors points for only $149. There are five destinations to choose from. A...Exact values of sin(60), cos(60), tan(60), csc(60), sec(60), cot(60), Find exact values of all trigonometric functions when the angle is 60 degrees,Check out...Apr 26, 2015 · What is the value of #sin -45^@#? How do you find the trigonometric functions of values that are greater than #360^@#? How do you use the reference angles to find #sin210cos330-tan 135#? Free math problem solver answers your algebra, geometry, trigonometry, calculus, and statistics homework questions with step-by-step explanations, just like a math tutor.Therefore, the value of sin 180 degrees = 0. The value of sin pi can be derived from some other trigonometric angles and functions like sine and cosine functions from the trigonometry table. It is known that, 180° – 0° = 180° ———– (1) 270° – 90° = 180°———— (2)Jun 8, 2015 · What is the value of #sin -45^@#? How do you find the trigonometric functions of values that are greater than #360^@#? How do you use the reference angles to find #sin210cos330-tan 135#?

Finding the exact value of the sine, cosine, or tangent of an angle is often easier if we can rewrite the given angle in terms of two angles that have known trigonometric values. We can use the special angles, which we can review in the unit circle shown in Figure 2.From the trigonometric formula, sin (90° – a) = cos a. You can now find the value of cos 60. You can write the above formula as: Sin (90° – 60°) = cos 60°. This gives you sin 30° = cos 60°... (2) Since the value of sin 30 is ½, Substitute this value in (2). Doing so, you get,Find the Exact Value sin (135 degrees ) sin(135°) sin ( 135 °) Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. sin(45) sin ( 45) The exact value of sin(45) sin ( 45) is √2 2 2 2. √2 2 2 2. The result can be shown in multiple forms. Exact Form: √2 2 2 2. The exact value of tan 30° is 0.57735. Tan 30° = 1/√3 = 0.57735. The value of tangent of angle 30 degrees can also be evaluated using the values of sin 30 degrees cos 30 degrees. Let us learn in detail in this article. …4. Write down the exact value of Sin 0°..... (1) 5. Write down the exact value of Cos 60°..... (1) 6. Write down the exact value of Sin 30°..... (1) 7. Write down the exact value of Tan 0°..... (1) 8. Write down the exact value of Tan 45°..... (1) 9. Write down the exact value of Cos 90°..... (1) 10. Write down the exact value of Sin 90 ...Find exact value of sin(105)Ans:= 4 6+ 2We know sin(A+B)=sinAcosB+cosAsinBHence sin105 ∘=sin(60 ∘+45 ∘)=sin60 ∘cos45 ∘+cos60 ∘sin45 ∘= 2 3× 21+ 21× 21= 2 23+1× 22= 4 6+ 2.

Then basic trigonometry tells us: sin θ = b a2+b2√ sin θ = b a 2 + b 2 and cos θ = a a2+b2√ cos θ = a a 2 + b 2. From this, cos θ = 2 5√ 5 cos θ = 2 5 5, but since we know it's less than 0 0, it is simply the negative, so cos θ = −2 5√ 5 cos θ = − 2 5 5.When it comes to determining used bicycle values, there are several venues that you can check. Before you get started, figure out the exact model and year of your bike to locate accurate information. This is more important when figuring how...Sep 29, 2016 · The trigonometric values we used in our derivation can be observed in the following right angled triangles: Hence sin45∘ = cos45∘ = 1 √2 = √2 2. Hence sin30∘ = 1 2 and cos30∘ = √3 2. Answer link. sin 165^@ = 1/4 (sqrt (6)-sqrt (2)) Some things we will use: sin (theta) = sin (180^@ - theta) sin (alpha-beta) = sin alpha cos beta ... Find the Exact Value cos(30)sin(60) The exact value of is . The exact value of is . Multiply. Tap for more steps... Multiply by . Raise to the power of . Raise to the power of . Use the power rule to combine exponents. Add and . Multiply by . Rewrite as .

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Trigonometry Examples Popular Problems Trigonometry Find the Exact Value sin (-60 degrees ) sin(−60°) sin ( - 60 °) Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. Make the expression negative because sine is negative in the fourth quadrant. −sin(60) - sin ( 60)Free math problem solver answers your algebra, geometry, trigonometry, calculus, and statistics homework questions with step-by-step explanations, just like a math tutor.\displaystyle{\sin{{\left({60}°\right)}}}-{\cos{{\left({60}°\right)}}}=\frac{{\sqrt{{3}}-{1}}}{{2}} Explanation: The exact values of \displaystyle{\cos{{\left({60 ...Question: Find the exact value of sin ( - 105°). Rewrite the expression sin ( - 105°) using the sum formula. Choose the correct answer below. O A. sin ( - 105°) =sin (60° + 45°) = [ sin 60° sin 45º - cos 60° cos 45º] OB. sin ( - 105°) = sin (60° + 45°) = [sin 60° sin 45° + cos 60° cos 45°] OC. sin ( - 105°) = - sin (60° + 45°) = - [sin 60° cos 45º + cos 60° sin 45°]This is one classic way to find the exact value of sin(18 degrees), i.e sin(pi/10). We will use the double angle identity for sin(2x), the triple angle ident...sin(60°)−cos(60°)= 23 −1 Explanation: The exact values of cos(60°) and sin(60°) ... If 6sinA + 8cosA = 10 , how to prove that tanA = 43 ? See the explanation below Explanation: 6sinA+8cosA = 10 Dividing both sides by 10 53sinA+ 54cosA = 1 ... The velocity of an object with a mass of 4kg is given by v(t) = sin3t + cos6t .

Explanation: For sin 135 degrees, the angle 135° lies between 90° and 180° (Second Quadrant ). Since sine function is positive in the second quadrant, thus sin 135° value = 1/√2 or 0.7071067. . . Since the sine function is a periodic function, we can represent sin 135° as, sin 135 degrees = sin (135° + n × 360°), n ∈ Z.Or you can say, the Sine of angle α is equal to the ratio of the opposite side (perpendicular) and hypotenuse of a right-angled triangle. The trigonometry ratios sine, cosine and tangent for an angle α are the primary functions. The value for sin 45 degrees and other trigonometry ratios for all the degrees 0°, 30°, 60°, 90°,180° are ...Step 1: Create a table with the top row listing the angles such as 0°, 30°, 45°, 60°, 90°, 180°, 270° and 360°and write all trigonometric functions in the first column such as sin, cos, tan, cosec, sec, cot. Step 2: Determining the value of sin: Write the angles 0°, 30°, 45°, 60°, and 90° in ascending order. The values of sin for ...Find exact value of sin (105) Ans: (sqrt(2 + sqrt3)/2) sin (105) = sin (15 + 90) = cos 15. First find (cos 15). Call cos 15 = cos x Apply the trig identity: cos 2x = 2cos^2 x - 1. cos 2x = cos (30) = sqrt3/2 = 2cos^2 x - 1 2cos^2 x = 1 + sqrt3/2 = (2 + sqrt3)/2 cos^2 x = (2 + sqrt3)/4 cos x = cos 15 = (sqrt(2 + sqrt3)/2. (since cos 15 is positive) sin (105) = cos (15) = sqrt(2 + sqrt3)/2 ...Method 2. Another method to derive the value of sineo 120 degrees is by using cosine functions. With the help of the trigonometry formula, sino (90 + a) = coso a ,we can determine sin 120 exact value. As we know, sino (90° + 30°) = sino 120 degrees. Hence, sin 120 degree = cos 30°.The exact value of sine of angle sixty degrees in fraction form is the quotient of square root of three by two, and it is written in below mathematical form in trigonometry. sin ( 60 °) = 3 2. The value of sine sixty degrees is an irrational number and its value is written in decimal form as follows. sin ( 60 °) = 0.8660254037 ⋯.Cos 30°= Sin 60° = √3/2. Cos 45° = Sin 45° = 1/√2. Cos 60° = Sin 30° =½. Cos 90° = Sin 0° = 0. Tangent: Tan 0° = Sin 0°/Cos 0° = 0. Similarly, Tan 30° =1/√3. Tan 45° …This video works to determine the exact values for the sin(30), cos(30), tan(30), sin(60), cos(60), and tan(60) using an equilateral triangle and the accompa...May 13, 2019 · The exact value of is . Step-by-step explanation: Recall that is a special angle that can be obtained using an equilateral triangle. The right triangle obtained using one of the lines symmetry was used to find the exact value of using SOH-CAH-TOA. The exact value of is . How to Find the Value of Sin 600 Degrees? The value of sin 600 degrees can be calculated by constructing an angle of 600° with the x-axis, and then finding the coordinates of the corresponding point (-0.5, -0.866) on the unit circle. The value of sin 600° is equal to the y-coordinate (-0.866). ∴ sin 600° = -0.866.Although the Bible does clearly show that people need to repent for all sins, there is no passage that says that all sins are equal; instead, the Bible shows some sins cause more guilt or damage than others.

Or you can say, the Sine of angle α is equal to the ratio of the opposite side (perpendicular) and hypotenuse of a right-angled triangle. The trigonometry ratios sine, cosine and tangent for an angle α are the primary functions. The value for sin 45 degrees and other trigonometry ratios for all the degrees 0°, 30°, 60°, 90°,180° are ...

Free math problem solver answers your algebra, geometry, trigonometry, calculus, and statistics homework questions with step-by-step explanations, just like a math tutor. Find the Exact Value (sin(60))(cos(60)) Step 1. The exact value of is . Step 2. The exact value of is . Step 3. Multiply. Tap for more steps... Step 3.1. Multiply by .Find exact value of sin (105) Ans: (sqrt(2 + sqrt3)/2) sin (105) = sin (15 + 90) = cos 15. First find (cos 15). Call cos 15 = cos x Apply the trig identity: cos 2x = 2cos^2 x - 1. cos 2x = cos (30) = sqrt3/2 = 2cos^2 x - 1 2cos^2 x = 1 + sqrt3/2 = (2 + sqrt3)/2 cos^2 x = (2 + sqrt3)/4 cos x = cos 15 = (sqrt(2 + sqrt3)/2. (since cos 15 is positive) sin (105) = cos (15) = sqrt(2 + sqrt3)/2 ...There is no definition for sin infinity. a function that takes the value between 0 and 1, or 0 and 90 degrees, returns to 0 degrees, then moves to 270 degrees in the 3rd …The angles are calculated with respect to sin, cos and tan functions. Usually, the degrees are considered as 0°, 30°, 45°, 60°, 90°, 180°, 270° and 360°. Here, we will discuss the value for sin 30 degrees and how to derive the sin 30 value using other degrees or radians. Sine 30 Degrees Value. The exact value of sin 30 degrees is ½.Find the Exact Value cos(210) Step 1. Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. Make the expression negative because cosine is negative in the third quadrant. Step 2. The exact value of is . Step 3. The result can be shown in multiple forms.Find the Exact Value sin(pi/4) Step 1. The exact value of is . Step 2. The result can be shown in multiple forms. Exact Form: Decimal Form:Use our sin(x) calculator to find the exact value of sine of -60 degrees - sin(-60 °) - or the sine of any angle in degrees and in radians. Exact value of sine of -60 degrees as a fraction. MenuExplanation: For sin 135 degrees, the angle 135° lies between 90° and 180° (Second Quadrant ). Since sine function is positive in the second quadrant, thus sin 135° value = 1/√2 or 0.7071067. . . Since the sine function is a periodic function, we can represent sin 135° as, sin 135 degrees = sin (135° + n × 360°), n ∈ Z.

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What are the values of sin 30, sin 60, sin 45, and sin 90 in numericals?In 1993, Mr. Arafat signed the Oslo accords with Israel, and committed to negotiating an end to the conflict based on a two-state solution. Hamas, which opposed …If we write opposite of the value of Sin degrees, we get the values of cos degrees. Because, Sin θ=1/Cos θ. Therefore we can write, Sin 0 0 = Cos 90 0 =0. Sin 30 0 =Cos 60 0 =½. Sin 45 0 =Cos 45 0 = 1/√2. Sin 60 0 =Cos 30 0 = √3/2. Sin 90 0 =Cos 0 0 =1. In the same way, we can write the values for Tan degrees.Free math problem solver answers your algebra, geometry, trigonometry, calculus, and statistics homework questions with step-by-step explanations, just like a math tutor.I have noticed that students cannot actually remember values of six trigonometric ratios (sin, cos, tan, cosec, sec and cot) for 0. , 30. , 45. , 60. and 90. . These values are used very often and it is recommended from my point of view that student should be able to tell the values instantly when asked. There is a proper method to memorize all ...Evaluate sin(-60 degrees ) Step 1. Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. ... The exact value of is . Trigonometry Find the Exact Value sin (60 degrees ) sin(60°) sin ( 60 °) The exact value of sin(60°) sin ( 60 °) is √3 2 3 2. √3 2 3 2 The result can be shown in multiple forms. Exact Form: √3 2 3 2 Decimal Form: 0.86602540… 0.86602540 …What is the value of #sin -45^@#? How do you find the trigonometric functions of values that are greater than #360^@#? How do you use the reference angles to find #sin210cos330-tan 135#?The exact value of Sin 180 Degrees is 0. Sin 180 Degrees is written as sin (180° × π/180°) in radians, i.e. sin (π) or sin (3.141592. . .). Trigonometry is a branch of Mathematics that deals with the length, height, and angles of a right-angled triangle. ... sin 60° sin π/3: √3/2: ….

Find the Exact Value sin(45 degrees ) Step 1. The exact value of is . Step 2. The result can be shown in multiple forms. Exact Form: Decimal Form:Pythagoras. Pythagoras' Theorem says that for a right angled triangle, the square of the long side equals the sum of the squares of the other two sides:. x 2 + y 2 = 1 2. But 1 2 is just 1, so:. x 2 + y 2 = 1 equation of the unit circle. Also, since x=cos and y=sin, we get: (cos(θ)) 2 + (sin(θ)) 2 = 1 a useful "identity" Important Angles: 30°, 45° and 60°. You should try to …sin 60° = √ (3)/2. sin 60 degrees = √ (3)/2. The sin of 60 degrees is √ (3)/2, the same as sin of 60 degrees in radians. To obtain 60 degrees in radian multiply 60° by π / 180° = 1/3 π. Sin 60degrees = sin (1/3 × π). Our results of sin60° have been rounded to five decimal places. If you want sine 60° with higher accuracy, then ... Calculate the value of the sin of 245 ° To enter an angle in radians, enter sin(245RAD) sin(245 °) = -0.90630778703665 Sine, in mathematics, is a trigonometric function of an angle. ... How do you use the angle sum identity to find the exact value of \displaystyle{\sin{{255}}} ? ... Get the value of \sin(60) from trigonometric values table. 0 ...Method 2. By using the value of cosine function relations, we can easily find the value of sin 120 degrees. Using the trigonometry formula, sin (90 + a) = cos a, we can find the sin 120 value. As given, sin (90° +30°) = cos 30°. It means that sin 120° = cos 30°. We know that the value of cos 30 degrees is √3/2. Therefore, sin 120° = √3/2. \[\sin{60} = \frac{\sqrt{3}}{2}\] \[\cos{60} = \frac{1}{2}\] \[\tan{60} = \sqrt{3}\]Find the Exact Value sin(30)+cos(60) Step 1. Simplify each term. Tap for more steps... Step 1.1. The exact value of is . Step 1.2. The exact value of is . Step 2 ... Free math problem solver answers your algebra, geometry, trigonometry, calculus, and statistics homework questions with step-by-step explanations, just like a math tutor. What is the exact value of sin 60, Example 4: using the exact values. Write down the exact value of \sin 45+\tan 60 sin45 + tan60. Express your answer as a single fraction with a rationalised denominator in its simplest form. Write down the exact trig value required. Show step. We need the exact value of \sin 45 sin45 and \tan 60 tan 60., The problem reads as follows. An exact value for cos36° can be found using the following procedure. Begin by considering sin108°. Note that 108 = 72 + 36 and use the sine sum identity. Also note that 72 = 2 ⋅ 36 and use double angle identities., Find the Exact Value sin(120) Step 1. Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. Step 2. The exact value of is . , I have noticed that students cannot actually remember values of six trigonometric ratios (sin, cos, tan, cosec, sec and cot) for 0. , 30. , 45. , 60. and 90. . These values are used very often and it is recommended from my point of view that student should be able to tell the values instantly when asked. There is a proper method to memorize all ..., Hint: To find the exact value of the given function, at first, we will find the value of \[\sin {60^ \circ }\]and \[\cos {60^ \circ }\]separately. Then using these values we can …, Free math problem solver answers your algebra, geometry, trigonometry, calculus, and statistics homework questions with step-by-step explanations, just like a math tutor. , sin(60°)−cos(60°)= 23 −1 Explanation: The exact values of cos(60°) and sin(60°) ... If 6sinA + 8cosA = 10 , how to prove that tanA = 43 ? See the explanation below Explanation: 6sinA+8cosA = 10 Dividing both sides by 10 53sinA+ 54cosA = 1 ... The velocity of an object with a mass of 4kg is given by v(t) = sin3t + cos6t ., The exact value of sin(45) sin ( 45) is √2 2 2 2. − √2 2 - 2 2. The result can be shown in multiple forms. Exact Form: − √2 2 - 2 2. Decimal Form: −0.70710678… - 0.70710678 …. Free math problem solver answers your algebra, geometry, trigonometry, calculus, and statistics homework questions with step-by-step explanations, just ..., \displaystyle{\sin{{\left({60}°\right)}}}-{\cos{{\left({60}°\right)}}}=\frac{{\sqrt{{3}}-{1}}}{{2}} Explanation: The exact values of \displaystyle{\cos{{\left({60 ..., Download Article. 1. Evaluate the following. The angle is not commonly found as an angle to memorize the sine and cosine of on the unit circle. 2. Write the expression in terms of common angles. We know the cosine and sine of common angles like and It will therefore be easier to deal with such angles. [2] 3., Rational values of trigonometric functions. I am using extensively trigonometric functions when an angle is given in degrees. Some of these functions like sine or cosine have rational values, for example, the well known example is that cos(θ) = 0.6 cos ( θ) = 0.6 and sin(θ) = 0.8 sin ( θ) = 0.8. However besides the case of multiplicity of ..., The exact value of cot(60) cot ( 60) is 1 √3 1 3. 1 √3 1 3. Multiply 1 √3 1 3 by √3 √3 3 3. 1 √3 ⋅ √3 √3 1 3 ⋅ 3 3. Combine and simplify the denominator. Tap for more steps... √3 3 3 3. The result can be shown in multiple forms. Exact Form:, Or you can say, the Sine of angle α is equal to the ratio of the opposite side (perpendicular) and hypotenuse of a right-angled triangle. The trigonometry ratios sine, cosine and tangent for an angle α are the primary functions. The value for sin 45 degrees and other trigonometry ratios for all the degrees 0°, 30°, 60°, 90°,180° are ..., There is no definition for sin infinity. a function that takes the value between 0 and 1, or 0 and 90 degrees, returns to 0 degrees, then moves to 270 degrees in the 3rd …, Free math problem solver answers your algebra, geometry, trigonometry, calculus, and statistics homework questions with step-by-step explanations, just like a math tutor., On the trig unit circle: sin 120 = sin (180 - 60) = sin 60 = sqrt3/2. Trigonometry . Science Anatomy & Physiology Astronomy Astrophysics ... What is the value of #sin -45^@#?, Now, to find the cos values, fill the opposite order the sine function values. It means that. Cos 0° = Sin 90°. Cos 30° = Sin 60°. Cos 45° = sin 45°. Cos 60° = sin 30°. Cos 90° = sin 0°. So the value of cos 90 degrees is equal to 0 since cos 90° = sin 0°. Angles in degrees., Exact values of sin(60), cos(60), tan(60), csc(60), sec(60), cot(60), Find exact values of all trigonometric functions when the angle is 60 degrees,Check out..., Exact values of sin(60), cos(60), tan(60), csc(60), sec(60), cot(60), Find exact values of all trigonometric functions when the angle is 60 degrees,Check out..., On the trig unit circle: sin 120 = sin (180 - 60) = sin 60 = sqrt3/2. Trigonometry . Science Anatomy & Physiology Astronomy Astrophysics ... What is the value of #sin -45^@#?, How to use the trig ratios of special angles to find exact values of expressions involving sine, cosine and tangent values of 0, 30, 45, 60 and 90 degrees? Example: Determine the exact values of each of the following: a) sin30°tan45° + tan30°sin60°. b) cos30°sin45° + sin30°tan30°. Show Video Lesson. , Explanation: assuming the values are in degrees, sin(45) = sin( π 4) = √2 2. cos(60) = cos( π 3) = 1 2. so. sin(45) + cos(60) = √2 2 + 1 2. = 1 + √2 2. Answer link. The answer is 1.20 sin45^"o"=0.71 cos60^"o"=0.50 0.71+0.50=1.20., \displaystyle{\sin{{\left({60}°\right)}}}-{\cos{{\left({60}°\right)}}}=\frac{{\sqrt{{3}}-{1}}}{{2}} Explanation: The exact values of \displaystyle{\cos{{\left({60 ..., Given the right angled triangle in the figure below with known length of side a = 52 and of the hypotenuse c = 60 the inverse cosine function arcsin can be used to find the angle α at point A. First, calculate the sine of α by dividng the opposite side by the hypotenuse. This results in sin(α) = a / c = 52 / 60 = 0.8666., Apr 28, 2022 · Find the value of sin 300 degrees? sin 300 = -sin 60 = -sqrt(3)/2 you can get this because using the unit circle. ... What is exact value sin480degrees? sin 480&deg ... , Trigonometry. Find the Exact Value sin (240 degrees ) sin(240°) sin ( 240 °) Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. Make the expression negative because sine is negative in the third quadrant. −sin(60) - sin ( 60), Solution. Using your knowledge of the values of trig functions for angles, you can work backward to find the angle that the brace makes: tan C tan−1 C C = 1 3–√ = tan−1 1 3–√ = 60∘. Example 2.3.10.2. Find the exact value of the inverse function of cos−1(0), without a calculator in [0, 2π), The values of sine and cosine of 30, 45, and 60 degrees are derived by analysis of the 30-60-90 and 90-45-45 triangles. If the angle is expressed in radians as a π / b {\displaystyle a\pi /b} , this takes care of the case where a is 1 and b is 2, 3, 4, or 6. , Explanation: sin690∘ =sin(720∘ −30∘) , = sin(4π− 6π) ... Calculate the value of the sin of 0.1 ° To enter an angle in radians, enter sin (0.1RAD) sin (0.1 °) = 0.00174532836589831 Sine, in mathematics, is a trigonometric function of an angle. The sine of ... It looks like you're using the 3rd-order term , but you need to use the ..., In 1993, Mr. Arafat signed the Oslo accords with Israel, and committed to negotiating an end to the conflict based on a two-state solution. Hamas, which opposed …, Trigonometry Find the Exact Value sin (60 degrees ) sin(60°) sin ( 60 °) The exact value of sin(60°) sin ( 60 °) is √3 2 3 2. √3 2 3 2 The result can be shown in multiple forms. Exact Form: √3 2 3 2 Decimal Form: 0.86602540… 0.86602540 … , What is the exact value of sin 60°? Enter your answer, as a simplified fraction. Solution: Given: sin 60° We know that sine of an angle is defined as the sine of an angle in a right-angled triangle is:. The length of the side opposite the angle is divided by the length of the hypotenuse.. In a 30-60-90 triangle, the sides are in the ratio 1: √3: 2. Thus adjacent: …, The trigonometric values we used in our derivation can be observed in the following right angled triangles: Hence sin45∘ = cos45∘ = 1 √2 = √2 2. Hence sin30∘ = 1 2 and cos30∘ = √3 2. Answer link. sin 165^@ = 1/4 (sqrt (6)-sqrt (2)) Some things we will use: sin (theta) = sin (180^@ - theta) sin (alpha-beta) = sin alpha cos beta ...