re". i0 Write the expression in rectangular form, x+ y i, and in exponential form, re 3n 15 + i sin 10 cos 10

Q: 2. Express each expression in a simpler form. a) cos 0 sec e b) tan 0 cos 0 c) tan 0 + cot 0 d) VI –…

A:

Q: OR = {(r, 0): 0 <r< 6 cos(30), 0 < 0 < n}

A: Follow the procedure given below.

Q: 14.) cos? 0 sin' 0 de

A: We have to find

Q: Simplify sin 37° cos 53º + cos 37° sin 53°. а. 0 b. 1 с. -1 d. 0

A: Given: sin(37ο)cos(53ο)+cos(37ο)sin(53ο)=?

Q: f(0) = e2i0 cos² 40 – e 210 sin? 40 in terms of complex exponentials. Then, evaluate f(0) de.

A:

Q: (a) cos(a + B) (b) sin(B al =

A: We will find the  required value

Q: 0 cos n0 do

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Q: T (b) fo 6 sin 20 cos² 20 ӨР

A:

Q: Establish the identity. e(1- sin? 0) = 1 sec Rewrite the left side expression by expanding the…

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Q: Reduce to the form a + bi: a. sin (-i); b. cosh (1); С. cSc (1 + i); d. sinh (3 + 4i)

A:

Q: Find the product of z1 & Z2, leave answer in trigonometric form: 235 (cos플 + isin) & z2 =: +i sin 3…

A: We know that for  z1 = r1 cos θ1 + i sin θ1  and  z2 = r2 cos θ2 + i sin θ2 z1·z2 = r1·r2 cosθ1+θ2 +…

Q: 22 r = 7 sin 0 + 50 cos O

A:

Q: tan (a-b) tan a=3/4, with a being in q 3 sin b= 3/5 with b being in q 2   give the exact answer…

A:

Q: 16 sin? (4V) cos³ (2/T), 0.

A:

Q: 5. Simplify the following expression! (1+2i)|3+ i[² (c +i· sin 6. COS |

A: That's easy. Have a great day!!!

Q: sin (A+B) cos(A-B)

A:

Q: [0.72(cos 235° + j sin235°)* 0.45(cos 84°+j sin 84°) b) Simplify give your answer in algebraic form.

A: Here, the given expression is: [0.72(cos 235°+j sin 235°)]20.45(cos 84°+j sin 84°)...(1) To simplify…

Q: a) Simplify the following expression: V-25 + 2i602 + 1(i6)8 + [9 + 8i| – 4(5+ 6i)v-36 b) Express…

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Q: 1. Simplify the expression cos z(sec a- cos z). COB C O cos? a O sin? a sin T

A: use trigonometric function properties

Q: 1 – sin? B 47. cos B cos B

A:

Q: r = sin 8 +2 cos?e

A: The given equation is r=sinθ+2cos2θ. Note that r=sinθ+2cos2θ is a polar curve.

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

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Q: 57 h. cos-1 (sin) 4

A:

Q: cos3(50) sin(50) de

A: To determine the integral.

Q: ind the exact value of the expression. sec(sin−1(5/13))

A:

Q: 12) sin? 0 +2 - cos? 0 = 3sin 0

A: (12) Given: - The equation is, sin2θ+2-cos2θ=3sinθ To solve: - The solution of the given equation.

Q: 1/2 sin e cos (cos a cosec 0) de TC (1-cos a).

A: Note that we have to show that the integral value is  π2(1 - cosα).

Q: 11. cos (x) = sin (x + 20)° %3D I Answer:

A: We will use the trigonometric identity written below to answer this

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

A:

Q: 6. cos(A+ B) cos(A – B) = cos² A – sin? B COS - -

A:

Q: Solve the equation for 0 if 0° < 0 < 360° 2 sin 6 - si n 26 = 0 %3D

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Q: 2л sin O te! 4+ cos 0 -do

A:

Q: Express the number -9 in the form R(cos(0) + i sin(0)) = Re where R> 0 and 0 ≤ 0 ≤ 2TT. NOTE: Enter…

A: Exponential and Polar form

Q: 2 2 (5 cos? r* sin 0 drdodo: Tame 0 01

A:

Q: sin(48) cos(48x) dæ : О576 O -2 O 2

A: We have to find the value of definite integral

Q: Express each one of the following in the standard form a + ib. 1 (1+ i)? (iii) 3 - i 1 (vi) 1- 2i…

A: vii)

Q: etermine the fifth roots of 32 cos 5 T 6 + i sin 5T 6

A: Solution :-

Q: 8 cos5(α)/(sin(α))1/2 dα

A:

Q: cos A 16-22. Show that = sec A is an identity. ´1-sin² A

A: To prove the identity.

Q: Write the expression in rectangular form x +y i and in exponential form re 4 6 COS + i sin 3

A:

Q: 25. The identity 2 sec? z has non-permissible values of: 1+ sin r 1- sin a Oz +an, n EI Ox ++an, nEI…

A:

Q: 11) cos? 0 = 2+ 2sin 0

A: Given query is to find the value of angle theta.

Q: Let z=x+iy be a complex number such that coshz+0. Then Re(tanhz) is equal to " sinhxcoshx…

A:

Q: Cim sin(4)it in(2411);+ Cos)K Cos(4)k

A: This question can be solved by applying the formulas of limit on first term and by directly applying…

Q: G. Determine the value of B that will satisfy the following. a) sin (4B + 10°) = cos 6B b) sec (3ß –…

A: we have to determine the following

Q: 3. Evaluate [7(cos 30° +i sin 30°) ][2(cos 90° +isin90°)].Write the product in rectangular form…

A: Explanation: Given that,

Q: : sin (20) de? What is a) 1 b) 0 1 c) d) TT - 2 f) None of the above 8.

A: