4. Express in the form a + jb, (i) 2(cos 30° +j sin 30°) (ii) 5(cos 57° -j sin 57°)

Q: 3. Solve: cos xdx + ( 1+ | sin ædy = 0 %3D

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Q: √3+2 px/3 ² √²³ (2² 10 (2 cos 0 - 3 sin 30) de dr

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Q: 2 y = A cos 4x + B sin 4x +sin 3x b) 7

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Q: 3. [(3t +r*)sin (21)dt /

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Q: Show that (1-)dy+(cos xsin x-sy")dr =0 is an exact equation. Hence, find its general solution. Hint:…

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Q: 5. S(sin3x + cos2x)²dx

A: To find : ∫sin3x+cos2x2dx

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

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Q: Find the solution of sin² (x) – 4sin (x) – 1 = 0 for all angles between 0 and 2n.

A: Since you have posted multiple questions, as per our policy we will answer first question. Please…

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A: the given equation is: sin2u=sinu we have to find the solutions of the given equation in the…

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A: Differentiate y=2cos2t2

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A: Given, function is

Q: sin (2t + 1) - dt cos? (2t + 1) 31.

A: Use trigonometric substitution method for solving the integral.

Q: (a) Show that the equation cos rdr + (1+ -(+)- sin rdy = 0 is not exact.

A:

Q: 8 Find L-- 8s2+6 sin Vt cos Vt COS V V등 sin y응t COS

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Q: 5. Find y', if y = 2cosx sin2x – sinx cos2x %3D

A: NOTE:according to company rules I need to solve first question when multiple questions are posted

Q: Find all solutions of the equation 2 cos x – V3 = 0. on interval [0, 27) x =

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Q: 10. Show that L(cos- 3t – sin“ 3t)= 36 s2+36

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Q: / – 9x* sin²(7y") = 9x* cos²(7y/") What is y(4) if y(0) = 8? %3D %3D

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Q: 5. Find y', if y 2cosx sin2x – sinx cos2x %3D

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Q: 7. S sin3 4 x cos5 4 xdx

A: To find the integration

Q: S cos(3r)(sin(3x) +5)10 dz Select one: (sin(3z)+5)" 11 +C O (sin(3r) + 5)"+C (sin(37)+5)" 33 +C…

A: Consider the integral: I=∫cos3xsin3x+510dx……1

Q: Express the number 4√√3 – 2i in the form R(cos(0) + i sin(0)) = Reit, where R> 0 and -≤0 ≤ T. NOTE:…

A: Given Problem:- Expres then number 43-2i in the form of Rcosθ+isinθ=Reiθ ,where R>0 and -π≤θ≤π

Q: 1) z = 6| cos 3T +i sin 2 +i sin 6 W = 12] COS 6 Find 2.

A: Hello. Since your question has multiple parts, we will solve first question for you. If you want…

Q: 27 Show that the equation cos? x – 3 sinx cosx +1=0has only four solutions in the interval (0; 2pi)

A: Solution is here

Q: 1 -~-² ( 5 (52² + 4) = = = √( ² ) 6' +4' sin2t.dt

A: As per the instruction, we will be answering the first question. For (1), We need to verify the…

Q: Use undetermined coefficients to find the particular solution to y" + y' – 6y = - 2000 sin(4t) -88…

A: Let's find.

Q: 3 8) 1--sin (2t) = sin' (t) + cos (t) sin(t) + cos(t)

A: Given,            1-12sin2t=sin3t+cos3tsint+cost

Q: 1. . Use the method of characteristics to solve the first order equation Uz – 2uy with u(x, x) =…

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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: 3. Determine a root of the equation sin(x) + 3 cos(x)-2-0 Using the Secant method correct to five…

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Q: Solve: sin 3r dr + 2y cos 3r dy = 0 %3D

A: First make the differential equation in seperable variable form, that is taking function of x with…

Q: .15 S sin²4y cos>4ydy

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Q: COS 10T - i sin 10TT 3 3 GT+ 3 of 學 4T COS 27 + 40 3 C1) - 1 2

A: Use trigonometric ratios

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Q: dr 5) J, (2z– 1)3/2 (2x – 1)3/2 4 cos( sin2( dr

A: Integration is the process of finding the anti-derivative function of the given function.…

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A:

Q: find dr/ ds r cos 2s + sin2 s = π

A: It is given that,r cos2s+sin2s=πWe have to find drds

Q: 4. Find all solutions to the equation 4sin x cos x = v2 in the interval [0,2]

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Q: Cos 4x b. .J dx,u=1+2 sin4x (1+2 sin 4 x )*

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Q: 1. sin (3z) cos5(3z)dz

A: Note -  Acc. to Bartleby guidelines, we are supposed to do only one question . If you want more to…

Q: 3 3m 2. sin ---- sin(20) = b. cos(20) = a.

A:

Q: 2. Evaluate the integral J cos (3x) sin°(3x)dx in two ways, one with u = u = cos(3x). Even though…

A: Given: Apply u-substitution method. Use two methods u=sin(3x)  and u=cos(3x)

Q: b) Use the hyperbolic identity cosh(2x) = 2 cosh? (x)–1 to solve 4 cosh(2x)- 22 cosh(x)+19 = 0.

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Q: 9. sin 2x cos x + cos 2x sin x %3D 1/2

A: To find all solutions in the interval (0,2π). sin2xcosx+cos2xsinx=-12

Q: do 6) I cos° 0 7 [(1- sin° 31)- cos3t dt 8) | tan (5x)· sec (5x) dx

A: Since you have posted multiple questions we solve first question for you  To get the solution of…

Q: The simplified form of cos G- 13x) + sin + 13x V2 cos 13z + 2 sin 13æ O v3 cos 13z + sin 13x O cos…

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Q: The position of a particle moving in a straight line is given by s(t) = e-*cos(5t) for > 0, where…

A: We have to find the necessary equation that must be satisfied.

Q: cos (2t) 23. sin' (2t) dt 3

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Q: 4. Solve for all solutions to sin 3xcos 2x + cos 3x sin 2x =1 on [0, 2

A: Given: sin3xcos2x+cos3xsin2x=1 Identity Used: sinacosb+cosasinb=sina+b

Q: 8. dr Cos dr |I+ sinr 9. 13 10. VH + 16 dt

A:

Ratios

A ratio is a comparison between two numbers of the same kind. It represents how many times one number contains another. It also represents how small or large one number is compared to the other.

Trigonometric Ratios

Trigonometric ratios give values of trigonometric functions. It always deals with triangles that have one angle measuring 90 degrees. These triangles are right-angled. We take the ratio of sides of these triangles.