5Tt Let == 6 10n +i sin 7 10л +i sin 14 and =2= Cos 14 7 Find the following. Write your answers in trigonometric form. Give exact values in your answers (not decimal approximations). (a) 21 2 O+i sin ()) JT cos = 0 (cos O + i sin ()) (b) -

Q: Express cos- (a) in terms of cos(2a). Express sin (a) in terms of cos(2a).

A: This question is of double angled identity.

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A:

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A: Given:  a) x=-3+5i Any complex number z=a+bi  has a trigonometric form  x=rcosθ+isinθ where…

Q: 14. Given 0 < 0< 2T, solve 2 cos 0 + 3 sin 0 = 3. 7T 11T 6. ○ 등, 똥 6 ○ 들, 등, 똥 2 6.

A: Give 0≤θ&lt;2π, solve 2cos2θ+3sinθ=3

Q: 7. Find the exact values of: a) sin ¹(1) b) tan-¹(0) 5-¹ (13) 2 COS

A:

Q: Given the following informationabout one trigonometric function, evaluate the other five functions.

A: Solution: Consider the given trigonometric function is sin θ = -45    and π &lt; θ &lt; 3π2 sin θ =…

Q: 5. a. Find all solutions for the following trig. equations. sin (2x)=√√3 cos x b. 2 cos²x2 sin² x +…

A: sin2x=3cosx

Q: Solve ( sin θ - 2r cos^2 θ) dr + r cos θ ( 2r sin θ + 1) dθ = 0 a. r sin^2 θ - r^2 cos^2 θ = c b.…

A: Given that sinθ-2rcos2θdr+rcosθ(2rsinθ+1)dθ = 0. The objective is to solve the given equation.

Q: 3- Represent in the form of x+ iy a) V8 (cos + i sin m) b) 6 (cos 7 + i sin7)

A:

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A:

Q: 3 T 3. Find the exact value of sin 8. 1 + cos 0 - cos e 1 = + cos = ± sin cos O tan 1 + cos 0

A:

Q: Express cos (a) in terms of cos(2a). Express sin (a) in terms of cos(2a). cos² (a) COS sin (a)

A: (a) We have to express cos2α in terms of cos2α.

Q: 9. cos 0 =: 24 * and n < 0 < 2n 25 sec 0 = sin 0

A: Use trigonometric ratio to solve

Q: cos20 Prove that 1 = sin 0 1+sin 0 cos e Hence, solve 1 = 2sin20 – 1 for 0° < 0 <360° 1+sin 0 Answer…

A:

Q: 2. Estimate cos (– 0.1) + cos 4

A: As per given question  We have to solve above question

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A: Given integral is: I=∫11-sin θ+cos θdθ

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A: Given :

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A:

Q: 4 TC 4) Find cos- given tan 0 2. where 0 <0 <- %3D 3.

A:

Q: 9. cos (21) di 10. 11. sin'x cos's de 12.

A:

Q: 3nt 3nt s = sin 2 + cos 2 %3D

A: # we are entitled to solve one question at a time , please resubmit the other question if you wish…

Q: 2. Write –2 cos x – 3 sin x in the form R cos(x – a) with -7 < a < T. Round to three decimal places.

A: Answer is given in asked form.

Q: 5. у %3D sin?(3x? — 1) 6. Р() %3D 4csc(sin3t) ans. y' = 6xsin(6x² – 2) ans. P'(t) =…

A: Topic = Derivative

Q: the sum of sin h 2x and cos h 2x

A:

Q: 4π 4π T Lat=₁ = 3( cos + + + sin ) and 2₁ = 6( cos + + + sin =) +i i COS- 7 Find the following.…

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: 1+ sin 0 . Verify cos O 2 sec e Cos A 1+ sin A

A: Our Aim is to verify 1+sin θcos θ+cos θ1+sin θ=2 sec θ -(i)

Q: cos 4B – cos 2B | 2 cos 3B sin В O -2 sin 3B cos B O -2 cos 3B cos B O -2 sin 3B sin B

A:

Q: 4. Given 0 <0 < 27, solve -2 sin? 0 + cos 0 +1 = 0. 0, 7 O 5,7, O 0, 5,7, 3 O

A: To solve -2sin2θ+cosθ+1=0, where 0≤0≤2π. Solution: We know that, sin2θ+cos2θ=1⇒sin2θ=1-cos2θ Given…

Q: 21) sin 0- 215 and cos 0>0 3V7 and cos 0 <0 23) csc 0-

A:

Q: Express the number 3√3 - 5i in the form R(cos(0) + i sin(0)) where R> 0 and -T≤0 ≤ T. NOTE: Round…

A:

Q: 2л 13л +i sin 7 and Z, = 6| cos 7 13л +i sin 14 Let Z, = 3| cos 14 Find the following. Write your…

A: It is given that, z1=3cos2π7+isin2π7 and z2=6cos13π14+isin13π14. (a) Compute z1z2:…

Q: 15 Find sin 2x, cos 2x, and tan 2x if cos.xr= and x terminates in quadrant IV. 17 sin 2x cos 2x !!…

A:

Q: 1- cos(0) (d) de sin (0)

A: We have to find integration

Q: a) sin 4pi/3   b) cos 4pi/3 c) tan ( -9pi/4)

A:

Q: 3. (a) Use an appropriate factor formula to express sin(x) + sin(3x) as the product of a factor of…

A: (3)According to question factor formula to express (sin x+sin3x)As we know that sin(A)+sin(B)=2…

Q: . is cos(cos^-1 1.7=1.7 true?     2. is sin^-1 (sin80*)=80* true?

A: We know the basic relations      cos(cos-1x)=x Because cos and cos-1 are opposite functions,…

Q: 18. Solve the trigonometric equation 2tan?x- 6 = 0 for 0 sxs 2n. A. " 5 7 11 6'6'6 * 2 4 ST '3'3'3…

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: + i sin 12 22 = 2| cos 12 5m + i sin 12 5. Let z1 = 4 cos and 12 Find z,2, and

A: Given complex numbers are in polar form. For multiplication of polar numbers, the magnitudes are…

Q: 18. The value of sin (7 +2) is equal to sin a cos z cos z - sin r

A: 18)

Q: 10л. 5T +i sin 14 5T 10T +i sin 7 Let 1 = 41 cos and =, = 8 cos 14 Find the following. Write your…

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Q: 3 10 28. tan cos Н. | 12 20 29. cos sin -1 I. T tan (sin- (-) J. - 4 K. -T

A: We are asked to match the following.

Q: Express the number 3√3 - 6i in the form R(cos(0) + i sin(0)) = Re¹0, where R> 0 and -T≤ 0 ≤ T. NOTE:…

A:

Q: 2. Find exact value of (a) sin-(-1) (b) cos-11 (c) tan-1 /3 (d) sin(sin¬' 0.8) (e) tan-'(tan ) (f)…

A: (a) Consider the given expression: sin-1-1 Sine gives negative one as it value at -π2. Therefore,…

Q: 13 a Express sin(0 + 30°) + cos0 in the form Rsin(8+ a), where R>0 and 0°<a<90°. Give the exact…

A: Solved below

Q: VI25 cos 7 - j sin 11 1. Simplify 47T Express answer in rectangular form. 5 cos + jsin 11 11 +jsin-…

A:

Q: 7Tt Find the exact value of sin 4 7t sin 4 %3D

A: The objective is to find the exact value.

Q: 2 + cos 0 = 1 + 2 sin² 0

A: The given equation is  2+cosθ=1+2sin2θ The given set of possible answers is  -π3,-π4,π6,π4,2π3,π,3π2…

Q: 1-St? cos at 2-(6 sin 2t – 5 cos 2t ) 3-[( 3 t5 – 2 t3 + 4 e-8t) 4-1 3+25 9 52-16. 25-3 35-3 35+9 5-…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

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.