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, , 27 3 I 37 57 6' 2' 2' 6 0, 11T T, 27 6. I 37 57 3' 2' 2'3

Q: 1+ cos 40 cos* 20 do = .4 do = (1+2 cos 40 + cos 40) d0 1+ cos 80 de 4 3 + 2 cos 40 + 1 cos 80 do 1+…

A: Fully solve the intregal with each step

Q: 12 and x terminates in 13 nd sin 2x, cos 2x, and tan 2x if sin x= sin 2x cos 2x %3D tan 2x %3D II

A:

Q: 2 += cos 3t 3 -- sin 3t 4 3. L 20s? – 103s + 423 6. 28(s – 5)(s? – 9) 20s? – 103s – 423 20s2 + 103s…

A:

Q: Show that (cos 0 + i sin 0)" = cos n0 + i sinne for n = 3 and n = 4.

A:

Q: sec(θ)=11/3

A: Please refer to the image below

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

A:

Q: 7 If 0° < 0 < 90° and cos 0 = , find sin 20. 11 ' 28/2 121 14/2 121 O 84V2 121

A: To find the value of

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…

A:

Q: 무 2. If 270° <θ< 360° and cos θ %3D 를, find sin 을. O -4 6 O -4

A:

Q: Let z1 = 4 (cos 7π/12+ i sin 7π/12) and z2 = 2 (cos 5π/12+ i sin 5π/12) Find z1z2. Find z1/z2

A: Recall:  z1z2=r1r2cos(A+B)+isin(A+B) z1z2=r1r2cos(A-B)+isin(A-B) We have, r1=4, r2=2, A=7π12,…

Q: Enter the EXACT value for each of the following. (a) cos( 0°) = and sin( 0°) = (b) cos( 45°) = and…

A: Answer is mentioned below

Q: Value of L is 16 $3+9s 16 O(1 + sin 31) 16 O (1 + cos 3t) 16 (1+ cos 3t) 3 (1 - cos 3t)

A:

Q: Show that (cos 0 + i sin 0)" = cos n0+ i sinne for n = 3 and n = 4.

A: Since you have asked multiple question, as per company guidelines we will solve the first question…

Q: If sin u  = 3/ 5 and sin v = 4/5  and that u and v  are  between  0 and π/2,   evaluate :     cos (…

A: given: sinu=35 sinv=45 and u and v are between 0 and π2. we have to evaluate cos(u-v)

Q: 1. Given z, = 5 cos 377 +i sin 37 and z2= 37 +i sin 2 find z,z2 where 0se< 2x. cos 2 2 37 +i sin 2…

A:

Q: 2. If 0° < 0 < 90° and cos 0 find sin 20. 3/55 32 V55 64 V55 32 3/55 64

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Q: 57 where 2 tan 0 = <0 < 3T 3 Find sin 20 7 24 24 25 24 25 25 24 4,

A: By using sin(2x) formula in terms of tan(x).

Q: 9 sin sin 2O° =Y 1o) cos cos 70 = a4 24 1)Sin Sin 7o = X 24 12) cos cos 20 = _ x %3D 24 24 20

A:

Q: If 0 = then 3 %3D sin(8) = %3D cos(e) = %3D

A: We have  this can be also written as

Q: If e 17/2- 2i =sin2 then z = %3D - 2i In(sin2) + 4kn -2 In(sin2) + 4kT - 2i In(sin2) – 4kn 2i…

A: Concept : eiθ =cos(θ)+i sin(θ)                  if θ=2kπ                    ei2kπ =cos(2kπ)+i…

Q: -24-4s e S COS os(28) – 7 sen(28) cos s+6 s2 + 49

A:

Q: Answer: The approximate value of sin 29° is O sin 29° s 1( 29x 2 180 6)+ O sin 29° V3 ( 29x O sin…

A: Please see the explanation below

Q: 15 1. If 180° < 0 < 270° and sin 0 = -, find cos . O 2V17 17 17/2 2 17/2 2/17 17 -

A: option (d) is correct

Q: 15 Find sin 2x, cos 2x, and tan 2x if sinx and x terminates in guadrant III. 17

A: Given that: sinx=−1517 To find: sin2x, cos2x, tan2x

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: - 47T then 3 - If 0 : sin(0) = cos(0) = COS Give exact values. No decimals allowed!

A:

Q: 5 2. In right triangle ABC, mzB = 90°. If tan C = 12 find sin A

A: Trigonometry Right angled triangle problem

Q: *(+²–1) cos[cosh (In r")]dr 4.

A:

Q: 3 Show that sin' 0 cos“ 0 1 1 cos (40) + 32 cos 128 cos ( 80). 128

A: To prove that,           sin4θcos4θ=3128-132cos4θ+1128cos8θ

Q: Consider (e cos 4 + ie sin 4) (11+12:) cos 4+ ie sin 4) (11+12i) 3DZ What is the general value of z?…

A: Euler's formula is given as that e^(ix) = cos(x) + i sin(x).

Q: 25л then 6. If 0 sin(0) - cos(0) =

A:

Q: If cos 0 = 0.9, find the value of cos 0 + cos (0 + 2x) + cos (0 + 4x). cos 0 + cos (0 + 2n) + cos (0…

A: Given, cos θ=0.9

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: 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: 27. Evaluate: cos 2) - sin 6 4 /3 /2 2 2 1 V2 V3 2 2 1 V2 2 None of the above. + |

A: Hence option (c) is correct.

Q: 1 then sin 20 is equal to 2 If 20 is in QIl and cos 30 cos 0 + sin 30 sin 0 V3 1 1

A: The given trigonometric problem is solved below in detail.

Q: 11 Ifx = Arc cos then x is equal to 1) 120° 2) 150° 3) 210° 4) 300°

A:

Q: 1 Find the exact value of cos(20) if sin(0) O 3 7 9. /3 3 1/9

A:

Q: 2 /5 If cos(a) = - with π<α< compute the exact value of the following: 2 cos(2a)=| sin 2 tan 2

A: To find the required values we need to use the double angle formula and the half angle formulas.…

Q: 13л +i sin 16 5л +i sin 8. 13л 5л Let Z1 = 10| cos and Z, = 2| cos 16 8

A:

Q: 11.Show that A cos (ω0t) + B sin (ω0t) can be written in the form r sin(ω0t − θ). Determine r and θ…

A:

Q: 3 Find sin 2.x, cos 2.x, and tan 2x if tanx and x terminates in guadrant II. 2 sin 2x %3D cos 2x tan…

A:

Q: 1 In 3n 1 sin (3x) [cos"-1 (3r) sin (3r) + 3(n – 1)In-2] %3D I1 = %3D - 3 What is I, ?

A: Given : In = (1/3n)  [cosn-1 (3x) sin (3x) + 3(n − 1)In-2 ]  I₁ =  (1/3n)sin (3x)

Q: One of the correct steps to evaluate A sin²20d0 [² B cos 40d0 C) None Ⓒ//ww D do + sin²20d0 Ⓒ = [ √…

A:

Q: 2 COS os²(5æ) sin*(5æ)dr 4

A: This is a problem of integration. Based on the general formula of integration we will solve the…

Q: Find the exact values of sın 20 and cos 20 for cos e on the interval 0° S 8590° sin 20= 0.7744, cos…

A: Use the identity sin2θ+cos2θ=1 to evaluate the value of sin θ. sinθ=1-cos2θ=1-372=1-949=4049=2107

Q: 2)50lve For Oso<27 -13 Sin n a =Coso

A:

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