Q1)a) Is the sigmal below periodic if periodic find its fundamental period g(1) = 3 sint+ cos + 2 cos (8t + 3 3 -

Q: 7. Prove that: (3) (a) (4) (b) sin20 cos20-1 in (-0) + cos (- 0) = cost -cote =

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Q: Do the functions y, = cos4t and y, = sin4t constitute a fundamer %3D The functions constitute a…

A: The given differential equation is y''+4y=0 the auxiliary equation is D2+4=0 D2=-4D=±2i therefore…

Q: Consider the Seq. {an} Which Begins cos(3), Cos(7) cos(1), cos (14), cos (17) COs(3) 3. 27 81 243 a.…

A: We are given the following sequence an which begins with cos(3)3, cos(7)9, cos(11)27, cos(14)81,…

Q: - 1, z = cos-

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Q: Thus, the graph of f(x) = 4 cos(X) (x, y) = ( ) (smallest x-value) (х, у) %3D ( (x, y) = ( )…

A: We will find the points as shown below

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: 4. Sketch a graph of y = -2 cos 2 for-2x SxS2n. v List 3 points below.

A: The given function is: The general form of the cosine function is: where, |a| represents the…

Q: 3 Evaluate: cos Arcsin ) - Arccos (-I COS 2 O Võ+v2 4 O -V6+v2 4 O v6-V2 4 O -V6-v2 4

A: The given expression is cosArcsin22+Arccos-32. We have to find out value of the given expression.…

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: 1- , S" cos(x)esin(x)-8y dydx

A: note : as per our guidelines we are supposed to answer only one question. Kindly repost other…

Q: In(cos ax) ? limx-0 In(cos bx)

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Q: 1-[t2 cos at

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Q: Q3-Prove that (cos303cos³ 0-3cos 0 sin? 0)

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Q: 6) What is the period of the function f(x) = 7sin(2x) – cos(5)? Is the function g(x) = 7xsin(2x) –…

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Q: e cosl – i e™ sin 1 + e¯ cos 1 - i e- sin 1 2 e cosl + i e™ sin 1 – e- cos 1 + i e¯I sin 1 -TT 2 e…

A: Simplify the given expression: Coshπ-i

Q: 3. Show that cos 30 = cos 0 – 3 cos 0. [Hint: Apply De Moivre's Theorem.] |

A: Given: verify that cos3θ=cos3θ-3cosθ according to given hint theorem cosx+isinxn=cosnx+isinnx

Q: 1 Prove that sec 03D Cos 0

A: Let P(x,y) be a point on a circle of radius r associated with the angle θ.

Q: 3. Show that the equation 1 + cos(x) – 2sin(=) = 0 has a solution in the interval [0, 7 /2].

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Q: Find all values of x in the interval (0, 27] that satisfy the equation sec2 x + 2 cos² x = 3

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Q: 9 If f(0) = cos 01 cos 02· cos 03 ... cos On + tan 0,}=- f (0) Show, {tan 0, + tan 02 + tan 03 +…

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Q: Prove using the IVT. tan-1x = cos-1x has a solution.

A: Given :                      tan-1 x = cos-1 xSolve :                     tan-1 x = cos-1 x…

Q: Use De Moivre's Theorem with n= 3 to express cos 3θ and sin 3θ in terms of cos θ and sin θ.

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Q: 5. Estimate to 4th place accuracy, i.e. within 0.00005 of cos(2º) using its Mac- xpansion. Justify…

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Q: - IF z = tan2 -1 y Show that x- ây

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Q: Find the length of the path over the given interval. (6(0 – sin(0)), 6(1 - cos(0)),

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Q: 3. Give upper and lower estimates (in terms of n alone) for sin nb COs na + valid for all a, b; show…

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Q: 7 Use the Intermediate Value Theorem and Rolle's Theorem to show that the equation 2 = sin z+1 has a…

A: use the intermediate value theorem and Roll's theorem to show that the eqautionx2=sinx+1has a…

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

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Q: Theory and Examples

A: limx→02x23-3cos x

Q: Show that cos bx = (eibx +e-ibx) and 1 sin bx :(eibx – e-ibx). 2i

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Q: 15 Suppose that tan a = TC <a<t. 2 and - Find the exact values of cos and tan 2 - JT Cos Undefined…

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Q: Compute e4 cos (r – 3) dr with two decimal places. Number

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Q: 7. Evaluate Arc cos(j2).

A: It is principal value.

Q: At what points do the local and absolute extreme values of the function (x) = 2 cos x- x^2 occur on…

A: We have to solve given problem:

Q: Use De Moivre’s Theorem with n = 3 to express cos 3θ and sin 3θ in terms of cos θ and sinθ.

A: To express cos3θ and sin 3θ in terms of cosθ and sinθ, using De Moivre's theorem with n=3. De…

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: (3) (a) Express cos(3r) in terms of sinx and cosr. (b) Prove that -cosz 1+cosI tan %3D (c) Sketch…

A: (3)  (a)  express cos(3x) in terms of cosx and sin x.       (b)  prove that 1-cos x1+cos x=tan2 x2…

Q: 12. Write an éxpression that gives all sölutions to the equation. COS X - SIn x 3= 2.

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Q: A string is stretched and fastened to two points at a distance 'x' of 10 cm. Vibration is started…

A: The given problem is to show the displacement of initial shape of the string from the given…

Q: Use Simpson's rule with n = 4 to approximate /" cos(2) -dr

A: Given: ∫16cosxxdx Here a=1, b=6 and n=4  h=b-an∆x=6-14∆x=54∆x=54

Q: The length of the curve r = sin² for the period 0 ≤ 0 ≤ π is 8 O 6 None of them O 2 O 4 O

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Q: Prove that (a) Pn (cos 0) = 2F1(-n,n+ 1; 1; sin²0/2).

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Q: 2. For the continuous time periodic signal x (t) = 2 + cos(# t) + sin( t) determine the fundamental…

A: Given continuous time periodic signal is x(t)=2+cos2π3t+sin5π4t                            (1) The…

Q: 2. Solve for the fundamental periodic and sample of the equation: x(n) = 2 cos 3. %3D

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Q: find y prime and y double primey=cos(x^2)

A: To apply chain rule and product rule to find the first and second derivatives of a composite…

Q: 6. In right ALMN with right angle at N, sin L 4x-0.22 and the cos M 2x+ 0.28. Determine and state…

A: Given; sin=4x-0.22 and the cosM =2x+0.28.

Q: 9 If f(0) = cos 0 c • cos 02· cos 03. ... cos On f'(0) Show, {tan 01 + tan 02 + tan 03 + ....+ tan…

A: We have fθ=cosθ1·cosθ2·cosθ3....cosθn                 ....(1) Now, we have a formula…

Q: 7. Prove that: ++) + sin; + e) = v3cose (3) (a) COS

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Q: 2. Prove that cos30 = (4cos'e - 3cos0) and sin30 = (3sine – 4sin e) using De Moivre's Theorem. %3D…

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