If 0 < α < π/2, and sin α = 1/3, evaluate the following in exact form.  a. sin α/2 b. cos 2α

Q: Find the exact value of the expression. sin 4 12 sin 4 12 CoS Cos 1 O A. 4 V3 О в. 1 О с. 2 O D. 1

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Q: if x is in III, and cos x= - 8/17. Determine the exact value of sin 2x and cos 2x

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Q: Let sin A = -3/5 with 270° ≤ A ≤ 360° and sin B = 12/13 with 90° ≤ B ≤ 180° and find the following…

A: Given sin A=-35 since, cosA=1-sin2A so,  cosA=1-925         =1625         =45 Also given, sinB=1213…

Q: Determine the Exact Values of the following expressions 1. sin210 2. (cos30) (2sin60) 3.…

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Q: What are the two values of k closest to 1 - 4 for which S sin? (x +4) – cos² (x + 4) dæ has a value…

A: The solution is given in the next step.

Q: Let sin A = − 8/17 with 270° ≤ A ≤ 360° and cos B = − 12/13 with 90° ≤ B ≤ 180° and find the…

A: Given

Q: Given the sin(a) = -8/15 and tan2B = 12/5, where a and 2B lie in the interval (3t, 71/2), compute…

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Q: Prove each of the following using identities, showing all work in the process: A.) cos(x+pi/3) +…

A: Given: (1)  cosx+ π3+ sinx-π 6 = 0 (2)  cos4x - sin4x  = cos(2x)

Q: Solve the following equations for 0 < x < 2n. 7. cos x = 3 cos x + 1 8. tan? x = 1

A: According to guidelines we should have been able to solve only one question at a time  #7

Q: Solve the following for 0, in radians, where 0 <0 <2n. 6 cos (0) +7 cos(0) – 7 = 0

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Q: If g(x) = x^2 sin(x), then what is g'(5)? Round to the nearest hundredth

A: Please see answer below

Q: In attempting to solve for x in the problem at the right, students responded with a variety of…

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Q: If sin(θ) = 0.788, then what is the approximate value of csc(θ)?   1.269   4.717   0.212   0.788

A: Given that sin(θ) = 0.788 To find the approximate value of csc(θ)

Q: Solve the following equation for values of 0 between 0 and 360° [Hint: Express (3 sin 0 + 4 cos 0)…

A: Given that 3 sin θ + 4 cos θ = 3 Express as 3 sin θ + 4 cos θ = R sin θ+α Then solve the equation…

Q: 6) Let sin 0 - for n <0 < Find the exact value of: %3D 2. a) cos 0 b) tan 0

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Q: -1 If 0 tan and 0 <0 < 180°, which of the following is equivalent to sin 6 11 O v3/2 O None of these…

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Q: Show that (1 – e") = 2 sin ( - a eil(a-r)/2]

A: To show 1-ejα=2 sinα2ejα-π2 , simplify left hand side expression and show equivalent to right hand…

Q: Find at least one solution to the following equation: sin(x² – 1) 1 – sin(x² – 1) sin(x) + sin²(x) +…

A: Given equation is, sinx2-11-sinx2-1=sinx+sin2x+sin3x+sin4x+... The objective is to find at least one…

Q: Solve the following inequality on the interval [0, 7]. 2 sin (0) + 3 cos(20) < 0

A: topic - inequality

Q: 1) Using the formula: cos(x + y) = cos x cos y – sin x sin y, prove in steps 1+cos 2 x that: cos? x…

A: In the question it is asked to calculate the solution of cos2x=1+cos2x2 using the formula cos(x+…

Q: What should be the first step in verifying the following identity? (Hint - look at the numerator)…

A: We have to check which one is satisfied

Q: If sin A = 3/5 with A in QI and cos B = -5/13 with B in Qull, find the following. Express your…

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Q: It is given that sin a + sin b = /5/3 and cos a + cos b = 1. Determine the exact value of cos (a -…

A: Since you have posted multiple questions in this question which are not interlinked so I have solved…

Q: 8 Let sin A = - 12 with 270° < AS 360° and cos B = with 90° < B s 180° and find the following. 17 13…

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Q: 3. Determine the exact value of the following. (K) (7n a) sin

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Q: Let sin A = - 15 with 270° SAS 360° and cos B = - with 90° s B < 180° and find the following. 13 17…

A: sin(A + B) = sinA cosB + cosA sinB  So we have to find cosA and sinB ,  Below, h= hypotenuse b= base…

Q: Find the exact values of sin 20 and cos 20 for cos 0= on the interval 0° <e5 90°. O sin 20- 0.7744,…

A: We know that, sinθ=1-cos2θ           ⋯⋯1sin2θ=2sinθ·cosθ         ⋯⋯2cos2θ=2cos2θ-1             ⋯⋯3…

Q: 3n 4. [K4] Given that cos: 11 == 0.6549, use an equivalent trig expression to evaluate sin" to four…

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Q: Find at least one solution to the following equation: sin(x² – 1) 1– sin(x² – 1) = sin(x) + sin (x)…

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Q: 1. Evaluate the following using (a) (2² – x) cos r dz

A: (a)  Given: ∫x2-xcosxdx

Q: For θ between 0° and 360°, find the two values of θ that satisfy the following.  cos θ = √2/2

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Q: 2-Find O for: y3tan? (cos x).

A: Using Chain rule we can solve the given derivative problem

Q: Let sin A = -3/5with 270° &lt;= A &lt;= 360° and cos B = - 8/17 with 90° &lt;= B &lt;= 180° and find…

A: Given: sinA=-35, where 270°≤A≤360° and cosB=-817, where 90°≤B≤180°. To find: sinA2 Solution: We have…

Q: expand the formula for sin(A+B)

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Q: Find the exact value of each of the following under the given conditions below. 4 T 1 <a<n; cos ß =…

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Q: Solve the following inequality on the interval 0, 7. 2 sin (A) + 3 cos(20) <0

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Q: d) For parts (d), (e) and (f), suppose u is in the interval (π/2 , π) and tan(u) = -2 Calculate…

A: Given,          tanu=-2

Q: b. Given that z = el®, show that z" += 2 cos ne. Hence, show that cos 50 = 16 sint 0 – 112 sin² 0 +…

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Q: Find (a) sin 2t, (b) cos 2t and tan 2t given the following: 1) cost = −5/13 , and π/2 0 3) tant =…

A: The detailed solution is given below Thank you

Q: Show that the following equation [ has a solution on (0, 2). 42-1 = πX 2 5 cos(-

A: The given equation,       4x-1=5cosπx2

Q: 1 Given that sin a = and cos b 3 , with a and b both in the interval 0, 7. Find sin(a – b)? O 4-6/2…

A: We use Trigonometry identities and ratios Sin(a-b) = sin (a) cos( b) -cos( a) sin( b)

Q: Given sin 0=- determine all possible values of 0 over the interval [-2n, 2n]. 2'

A: Given is the expression sinθ=12. We need to find the values of θ in the interval  -2π,2π Use the…

Q: Let sin A = − 15/17 with 270° ≤ A ≤ 360° and cos B = − 12/13 with  90° ≤ B ≤ 180° and find the…

A: It is given that, sin A=-1517 with 270°≤A≤360°.             and  cos B=-1213 with 90°≤B≤180°.We ahve…

Q: 2 cos2 (x) + 3 sin (x) – 3 = 0 b) tan (3x) = 1

A: 2cos2x+3sinx-3=0, 0≤ x&lt;2πRewriting, we get:-1-2sin2x+3sinx=0Solving by substitution:sinx=12,…

Q: -8 2. Given that sin a = and 15 12 tan 26 5 where a and 2B lie in the interval Зл, evaluate the…

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Q: uppose θ is in the interval ( π/2 , π) and sin(θ) = 1/5 . Evaluate the given quantities exactly, and…

A: sin θ = 15cos2 θ = 1 - sin2θcos2θ = 1 -(15)2 cos2θ = 1 -125cos2θ =2425cos θ = 265

Q: If n e N, then (1 + i V3)" + (1-iV3)" is equal to: إختر أحد الخيارات NTI .a 2" cos 3 None of these b…

A: To Determine :-  If n ∈ ℕ , then  1 + i 3n +  1 - i 3n is equal to :

Q: 1. Find the values of sin 20, cos 20 and tan 20, given: 9 3n a. tan 0 if n<0 < 40 2 3n b. sin 0 if <…

A: Giventanθ=940 ifπ&lt;θ&lt;3π2sinθ=-12 if 3π2&lt;θ&lt;2π.To findsin2θ, cos2 and tanθ

Q: 3. Find the O to the nearest degree if and with if cos 0= -0.8910 and Q II with 0<0<360°.

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Fundamentals of Trigonometric Identities

Trigonometric Identities are the equalities that involve trigonometry functions and hold for all the values of variables given in the equation.