/2 6 csc 0 a) [" r° cos 0 dr de 7/4

Q: 18 If csc(x) (in Quadrant-I), find 7 = s(2x)% = COS %3D

A: We have to find the value of cos2x.

Q: (-9)" (2n)! (a)e³ (b) cos 3 V3 (d) sin 3 (e) None (c) cos 2

A: The given series is ∑n=0∞(-9)n(2n)!

Q: 4 cos (m) – 4 cos (m) +1 sin (m) 2 dm

A:

Q: %3D 6. Given 0<0< 2T, solve cos 0 = cot 0.

A: The given question is taken from the above form the solution of the trigonometry equation in which…

Q: Find the points of intersection of the graphs of the equations  r = 1 − cos θ,    r = 1 + sin θ

A: To find θ, we equate the graphs.

Q: (a) {(-} )} (b) {cos kr} (c) {3k}

A:

Q: Evaluating √9-x² dx using trigonometric substitution will lead to: -3 [*1/2 cos²0de A 0 Ⓡ IS!" B 18…

A:

Q: Solve ax? cos xcos 2y дхду

A:

Q: -5 c) Given sec 0 = 4 cos? 0 = ? tan? 0 = ? sec (-0) = ?

A:

Q: Convert r = 6(sin(0) + cos(0)) to an equation in rectangular coordinates in terms of x and y.

A:

Q: cos 0 = –0.1672.

A: As we have a negative value for cos θ, θ must be in second or third quadrant.

Q: Solve for A +능 D %3D B If: A=V8 (Cos ti Sin) %3D 8 = (1+i) c : V2+2i D = 3[2.5 cis los°- 3.3 cis 60]

A:

Q: Find a rectangular form of the equation. r(7 cos 0 + sin 0) = 4

A: To convert a polar form to rectangular form the following formulae are used.

Q: 2.)S csc-³«(cosa)³da

A: Given ∫csc-3 α (cosα)3dαTo evaluate the integral:

Q: 16 sin? (4V) cos³ (2/T), 0.

A:

Q: 2. c=² (cos 0 - i sin 0) B e(cos 20 + i sin 20) C Cos 20 – i sin 20 e² (cos 0 – isin 0)

A: We will use the following Identity

Q: *T/2 10 cos(0) r dr de

A:

Q: [(6+3:)cos(1+ 42)dz

A: Given: ∫6+3zcos1+4zdz

Q: 2 2 cos 0 d0 V1 – sin 0

A: Given:        ∫0π2cosθ1-sinθdθ substitute u=1-sinθ→dudθ=-cosθ→dθ=-1cosθdθ      =∫10-1udu…

Q: a) Express 16sin 0 in the form a sin 0 + b sin 30 + c sin 50 , where a, b and c are constant.

A:

Q: (i) Express -5 sih 0 + 12 cos 0 in the form R cos(0 + a), where R>0 and 0<a < n. Give the value of a…

A: Okay I am solving first question as you mentioned.

Q: | 24 a° cos(2) dæ =, %3D

A: Given: I=∫24x3cosxdx For evaluating given integral, we use integral by parts theorem According to…

Q: 6. (a) 2 cos?t (b) 3 sin 2x

A:

Q: -2п a) cos 3 b) cot 45° 3 с) у%3D sin-1 /2 d) y = arccos 2.

A: Since you have posted multiple subparts, as per our policy we will answer first three subparts.…

Q: (A) B (C) (D) **/2 18 [*/ ces **/2 cos²0d0 18 sin²0d0 cos²0d0 0 of the 0 **/2 $ cos²0d0

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Q: find 0 2 Cos ☺ t 2= 3

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Q: Find fo, fe fe if fp.0,4) p cos sin 0 %3D

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Q: (16sin0-5)cos&de OS V121-4sin? 0

A:

Q: ·(플) 54. cos = cos ( T + 2

A:

Q: Find cos(u/2) if cosu=0.153 and u is in Quadrant-IV. round to the 4th decimal place cos(u/2)=

A:

Q: 2) Find f' (=), f" (A), f" (E) given f (0) = sin 30 cos 0

A:

Q: 7/2 sin e cos (cos a cosec 0) d0 TC (1-cos a) 2 -Cos Te/2-

A:

Q: r = 17 sin 2t i - 17 cos 2t j

A: Given equation r= 17 sin 2t i- 17 cos 2t  j

Q: The period of y = 3 cos 5x is 2 7I 2 T/5 2 1/3

A:

Q: fo 13. cos (0) – 5 sin (0) d0 COS

A:

Q: 3. Given 0 < 0< 2T, what are the extraneous solutions for the equation tan 0 sec 0 = 1?

A:

Q: Graph the epitrochoid with equations x  =11 =cos t - 4 cos(11t/2), y = 11 sin t - 4 sin(11t /2)

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Q: 2 cos 0 2. Write r = as an equation in rectangular cos 0-sin 0

A:

Q: - 3i TC - Suppose z=V 2| cos -i sin Find : 4 COS - - 4 3-31 2 3+31 2. -3+31 -3-31

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Q: r' = cos 0

A: The detailed solution is as follows:

Q: /2 89 cos t 9. dt = 1+ sin?t If q sec e de, then a = b = and g =

A:

Q: 2. A c² B c(cos 20 + i sin 20) C Cos 20 – i sin 20 D c(cos0 – isin 0) ? (cos0 -+ i sin 0) B D CO

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Q: de I cos? 0 2

A:

Q: 3T 7. (a) sin (b) cos

A: 7. a) sin3π4 Use the following identity                                                        sin x…

Q: Find the points of intersection of the graphs of the equations. r =1+ cos0 10) r =1-sin 0

A: Given, r = 1+cos(θ)  and r = 1-sin(θ)

Q: Evaluating 9-x² dx using trigonometric substitution will lead to: A of th (A) cos²0d0 [*/ cos²0de Ⓒ…

A:

Q: 2 55. y = cos(-)

A:

Q: 2. sin 8 = 42 P(0) is in the second quadrant

A: Given θ lies in the second quadrant We know that sinθ , cosecθ are positive in the second quadrant…