Find all the roots, of 2=+1+V3j A =D/2 (cos +j sin-) - B z=V2 (cos (-+ka) +j sin ( + ka)), k=-1,0 z=V2 (cos ( + 2ka) +j sin ( 12 + 2ka)), 12 - z=V2 (cos (+ ka) +j sin ( + ka) ), k=0, 1 12 12

Q: Prove that the equation sinx = 0.3 has at least one solution in the interval (o, ~).

A: Given:sinx=0.3

Q: 3. The integral of sin24x cos4x dx is a. (1/4) sin³ 4x + C b. (1/3) sin³ 4x +C c. (1/12) sin³ 4x+ C…

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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

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Q: Find all solutions of the equation in the interval [0, 2x). 2 cos x-1 = 0 5T O A. 3' 3 - T 3n 5n 7n…

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A: Let's find integration of given function.

Q: Find all solutions of the equation in the interval [0, 2x). V2 cos 2x = 2 3n 5n 7t O A. 4' 4 - - 4 4…

A: We have to find the solution

Q: 5. Show that cos (sin 2x) + sin (cos-1 2x) = (V2-2x)(VZ+2x) -

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Q: Prove using the IVT cosx = cos-1x has a solution in (0, 1).

A: cos x = x   rearrange to x - cos x = 0

Q: Place these trig equations into general form: 1. y = sin (4x + 3π/2) + 2 2. y = cos (3x - 6/7) 3.…

A: According to our guidelines we can answer only three subparts, or first question and rest can be…

Q: Show that sin 3x and cos 3x are orthogonal on [−π, π].

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Q: What substitution should be used to solve the integral x²dx |4+9x² O sin u=3x/2 sec u =2x/3 O sec u…

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Q: Solve exactly over the interval 0 ≤  θ  ≤ 2π 1. √3 Cosθ- 2sinθ cosθ = 0 2. Cos(θ/2) - cosθ = 0…

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Q: Therefore, YZ-F Find the coc 1. (-2, 3, 5) an

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

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Q: Prove | cosz |2 = cos²x+ sinh²y.

A: To Prove: cos z2=cos2x+sinh2y

Q: Solve the given differential euation: dr/dθ+rtanθ=10cosθ. 1.r=(10θ+C)tanθ 2.r=(10θ+C)cosθ…

A: In this question we have to solve the given differential equation.

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Q: a) By using convolution theorem, show that 1 (sin 3t – 3t cos 3t). 54 1 L-1 (s² + 9)2

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Q: Find all the roots of z²= - /3-j A z=2 (cos +j sin-) B z=/2 (cos (- =+ 2kn) +j sin ( 12 + 2kn)), 12…

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Q: Prove That 4 Sin ³²A - CoS 3 A +4 Cas³ A - Sin 3 A = 3 Siny A

A: We need to prove: 4sin3A.cos3A+4cos3A.sin3A=3sin4A

Q: solve for allvalues of x in the interval 0 ≤x≤2π:  2-2sin^2 x+3 cosx=-1

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Q: The second-order difference equation Yk+2 - 3yk+1 + 2yk = 2 sin(3k) (4.164) has the homogeneous…

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Q: Show that the equation 2x + cos(x) = 1 has exactly one root. (IVT and Rolle's Theorem)

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Q: The simplified form of cos ( - 5z) 5z) + sin 6 52) + sin (; + 52) O v3 cos 5x + v2 sin 5x O v2 cos…

A: This can be evaluated as:

Q: Solve for a root/roots of the functions 2. x2 – 3 sin x + 2 In(x + 1) = 3. 5 Applying both a.…

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Q: Prove that the equation sinx = 0.3 has at least one solution in the interval(o, π/2).

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Q: Evaluate the integral. sin (8t + 16) dt cos (8t + 16) sin (8t + 16) dt = cos (8t + 16)

A: Solved below

Q: 2) Find all solution of the equations in the interval [0,2x]. a) 2sin 30+ 12 = 0 b) (cosx- 1)(sin x…

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Q: Which of the following is a cubed root of (-/3 - 9? (A) 21°[cos(8z9) + i sin(8z9)] (B) 21[cos(7x/9)…

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Q: - Find all solutions for 4 cos x+V3 = 2 cos x if 0<x<2n. %3D

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Q: capacitor is constructed with two parallel metal plates each with an area of 0.61 m2 and separated…

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Q: 19. 2 sin 3x = V2 %3D 21. 2 cos (2x + 1) = 1 23. 2 sin (4x - 1) = 1 3x 25. 2 cos %3D EN =

A: The give trigonometric equation is: 2sin3x=2    ....(1) As we know that if the trigonometric…

Q: The suitable substitution to evaluate the integral cos°(2x) dx is 5(2x) 3 csc°(2x) u = sin(2x) u =…

A: First, simplify the integrand and use the substitution method

Q: Find the length of the path over the given interval. (5(0 - sin(0)), 5(1 – cos(0)) ), 0 < 0 < 2n

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Q: Q4:B/Simplify [cos 20-i sin20][cos 30+ i sin301² [cos 40+ i sin40³[cos 20-i sin2015 using De…

A: Formula Used-  De Moivre's theorem: cosθ+isinθn=cos nθ+isin nθ cos mθ+isin mθcos nθ+isin nθ=cos…

Q: Why is V /5+ 5 tan² 0 = v5 sec² 0? Because Vtan 0 = sec 0 Because 1+ tan² 0 = sec² 0. • Because sec?…

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Q: 9 Prove Sen 4t 4 cos3t sint-sin3t cos t.

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A: To find the intersection point two curve we have to find r,θ by solving given curve.

Q: Compute sin (3r)dr (25z4+1)2 -

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Q: 2 Find the points of intersection between r=2 cos20 and r = 1- cose

A: given r2=2 cos 2θ and r=21-cosθwe need to find the intersection between two polar curves

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Q: Approximate all solutions to 8-cos(x)² – 6·cos(x)+1 in the interval [0°,360°) x = V degrees Round…

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Q: Evaluate: cos32xdx cos³2x - +C 6. cos2x (A) cos32x +C cos2x B sin2x sin32x +C 6. = 2 sin32x + C 6.…

A: Given query is to find the integral.

Q: The solution of some second order linear DEQ is exp(-7x)[5sin(1x)+ 7cos(1x)] which can also be…

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