9. Suppose that A is such that sin A = 0 and cos A = -1 Find the exact values for each of the following expressions: (a) sin ( A+ 3 (4+) (b) cos

Q: 9 If f(0) = cos 0, ·cos 02· cos 03 ... cos 0n .... .·. f' (0) f (e) Show, {tan 01 + tan 02 + tan 03…

A: Given that we have to prove where

Q: 5. (a) Expand (1+x) and hence find the value of (1.02) correct to 4 decimal place 1+sin 0 m-1 1-sin…

A: First expand 1+x4 then find the value of 1.044 Using the identity, a+b4=a4+4a3b+6a2b2+4ab3+b4…

Q: 8. 4 sin(at +b), where a and b are constants.

A:

Q: Show that (1-)dy+(cos xsin x-sy")dr =0 is an exact equation. Hence, find its general solution. Hint:…

A:

Q: 3. * S cos(3z)sin1º(3z) dz A 1 C (sin(3z))10 + C 3 (cos (3z))10 + C - -- В 1 (cos (3z))'1 + C 33 1…

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Q: 1) Verify the power reducing formula, cos-x= 0:1 holds true for x = and x= =.

A: Here I am attaching image so that you understand each and every step.

Q: 5. Find the solutions to sin x tan x = sin x on 0<x<360° 6. Find all the solutions to 2cos(2x)–1=0…

A: Use the values of trigonometric values of some pre defined angles.

Q: 1 In [cos"-1 (3x) sin (3x) +3(n – 1)I-2] 3n 1 h= sin (3r) %3D What is I, ? I.

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Q: 5. Find all solutions to 1+ sin sin 3x = cos cos (0.25x) such that xE[0,r]

A: The best way to do this is to use some numerical method to solve this. It is not feasible…

Q: 1 9. In the proof that (sin-1x) = that sin(sin-1 x) = x. It is also true that sin-(sinx) = x; could…

A: Differentiation of function gives the change of function with respect any variable. The inverse…

Q: 06:- Find the result of the following. (Choose two only) 4 1- 2-Si(Vx+ dt OLLI x² 3- 7 sine do

A:

Q: If k0 then the trigonometric integral [ 3 sin³ (kx) dx is equal to [−sin(kx) + sin³(kx)] + C the…

A: To evaluate the integral.

Q: f(A) is an odd function, and deduce that for each x E R the value of the c) Show that integral 3A…

A: From part (a), the function f⏞λ is defined by f⏞λ=i2π3λcos3λ-1λ2sin3λ Relacing λ by -λ,…

Q: 15 and x terminates in guadrant III. 17 Find sin2x, cos 2x, and tan 2x if sin x= - sin 2x cos 2x %3D…

A: The solution is given in the next step.

Q: 1.)When m is odd, we can integrate sin" (x) dæ by letting u cos(a). Why does have to be odd for this…

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Q: 10. Show that L(cos- 3t – sin“ 3t)= 36 s2+36

A:

Q: 1. Eliminate the arbitrary constants on the given equation: -= C, cos 3r + C2 sin 3x

A: Elimination of the arbitration constants

Q: 32. If 2 sin 0 cos 0 cos 0 =0, where 0 <0 < 2n, then the exact values of 0 are 57 0, 3 O0, 5. 7, ,…

A: Given : 2sinθcosθ - cosθ = 0 Where, 0 ≤ θ ≤ 2π To find : Exact value of θ?

Q: 4. Derive error-bound formulas for the following expressions. i) cos(x) – sin(x) ii) In(x) + sin-1 y…

A:

Q: 9 Find 0 if 0<0 < 2n and: d sin 0 = 1 h cos? 0 = i tan 0: i tan? 0 = 3

A: To find θ if 0 ≤ θ ≤ 2π  sin θ = 1cos2 θ = 12tan θ = -13tan2 θ = 3

Q: 3 8) 1--sin (2t) = sin' (t) + cos (t) sin(t) + cos(t)

A: Given,            1-12sin2t=sin3t+cos3tsint+cost

Q: (1) Evaluate the following functions 1. In(3-i6) 3. cos (1+i3) , 2. e(0 52) , 4. tanh (2-i5)

A: As per guidelines, we solve only first question. 1. Given      ln3-i6

Q: 3 sin x If f(x) then 1+ cos x f'(x) = f'(1) =

A: topic -derivative of a function

Q: IFS(x) = - sin(x), then S ® (1) is equal to - sin(x) B) - cos(x) sin(x) O cos(x)

A: We have to solve

Q: 4) Find when y? – x² + cos(x + y) = 0

A:

Q: 4. sin M= 20 16 30 5. tan L = 6. cos Z = 16

A:

Q: 2. If 90° < 0 < 180° and cos 0 =-, find sin. %3D 11/3 11/3 3 ) - 3V11 11 O 3/11 11

A: We know that the trigonometric identities :  cos x = 1 - 2 sin2 (x/2)

Q: 1) Using the formula: cos(x +y) = cos x cos y - sin x sin y, prove in steps that: cos? x = %3D 1+cos…

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Q: 1 with in Ql , find sin B = B If cos B B Cos 3- 2/2 6 3- 2/2 Cos B COS 22 3 B cos 3 + V3 3 + 3 Cos 6…

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Q: S cos(3z)sin1º(3z) dz A 1 (sin(3z))10 + C 3 C 1 (cos (3z))10 + C 3 -- 1 D 1 (cos (3z))'1 + C 33…

A:

Q: 2. Eliminate all the arbitrary constants in the equation as follows: y = Ae2x – e-5* (B cos 2x + C…

A:

Q: Suppose sin(0) = and 0 < 0<T/2. Compute cos(0). (Hint: SOH-CAH-TOA) V3 3 3

A:

Q: Suppose that sin(a) = 4/5 and cos(b) =4/7 define in the first quadrant, determine tan(a+b). (round…

A: Given, sin(a) = 4/5 ------equation 1 cos(b) =4/7 ------equation 2

Q: Find the value of k if 1 х cos(3x) dx 1 3* x sin(3x) + — сos (3x) + C. k

A: .1. ʃ (u.v)dx= u ʃv.dx - ʃ(d/dx(u) . ʃv.dx)dx       Where u and v are function of x 2. ʃ sin(ax) dx=…

Q: Find the exact values of sin 20 and cos 20 for cos 0= 3 on the interval 0° s es 90°. 18 35 cos 28-…

A: cosθ=318    ,  0°≤θ≤90° By using the identity sin2θ+cos2θ=1, we get…

Q: 4. Find the exact values for each of the following. а. sec-1 b. sec-(-V2)

A: The detailed explanation and answer is given below:

Q: 4) Differentiate each of the following: a) y = - cos²x c) f(0) = sin(20 — π) b) y = sin(20) - 2…

A: Differentiate the following  a) y=-cos2x b) y=sin2θ-2cos2θ c) fθ=-π2sin2θ-π

Q: 7.32. Prove that for 05sr, -( . ) cos 2 cos (a) a(e -a) = sin 3r sin ba (6) (r-) - 7.33. Use Problem…

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Q: How do you solve this?

A: Given that cos x = 1/3 and x is in the interval (0, π/2).sin y = 1/2 and y is in the interval (π/2,…

Q: 2. If x = 2 sec 0 and 0<0< T/2, then %3D (a) sin 0 = (b) cos 0 (c) tan 0 =

A:

Q: 1. Find the exact value (not a decimal approximation) for sin(22.5°) (Hint: 22.5 = 45/2)

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Q: For how many a E (0, 1) will sin(x) + a sec(x) = cos(x) + a csc(x) have at least two distinct…

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Q: 2 Recall thal cos-x= arccos x, Find /2 X Sin (cos x) dx. C.

A:

Q: 6. In right ALMN with right angle at N, sin L 4x-0.22 and the cos M 2x+ 0.28. Determine and state…

A: Given; sin=4x-0.22 and the cosM =2x+0.28.

Q: 3. (a) Use the substitution x = 2 tan 0(-1/2 <0 < T/2) in the expression T/V4+x2 and show the result…

A:

Q: Find cos (0 + p) given that cos 0 = and cos p = and that 0 and p are %3D between 0 and n/2.

A:

Q: How do you solve this and can you show me step by step?

A: Simplify the equation to get a quadratic in cos x.

Q: -1 Find y' where y = 22 sin-(cos (9 æ)) – tan (6 æ) Answer: -198 sin(9 x) 1 || V1-cos2 (9 æ) 1+36 x2…

A: To find y'