1. (a) Give the four angles βι, β2, β3, and β4 between π and 3π such that lcos(Al 1/2 for i [1,4 (b) Give the corresponding reference angle for each Bi. (c) which β's also satisfy cos(A)-1/2?

Q: -1x 54cos If cos -1 00, prove that b. a x² 2xy ,2 = sin C. COS a+ ab %3D 2

A: Introduction :

Q: 15. Find a) fxedx b) dx using the substitution of x- cos t.

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Q: 1. Evaluate COS dır V1- 2 sin æ (7/6 (a) ( - z)e* dz (b)

A: To evaluate the given definite integrals.

Q: The second derivation of y = cos(2x)

A: Given  y = cos(2x)   ........ (1) We know that  d (cosx)dx= -sinx        ........ (a) and  d sinxdx…

Q: 2) find the radius and coordinate center for the equation 2x42y+10y-12х-20-0 3) prove that sin 2x…

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Q: Given that the characteristic equation has the following roots , what is the complementary solution?…

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Q: 3 Find the exact values of s in the interval [0,2x) that satisfy the given condition cos 2s = л 11т…

A: Topic : trigonometry

Q: Solve (by separation of variables) the following problem du = 0 ; x E R , t> 0, t > 0, - и(х,0) =…

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Q: If cos t = - and t is in the 3rd quadrant, then sint = %3D V32 6 V40 6 V32 2 V32 6 O V32 2

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Q: 5. What is the exact value of cos(™)? y (0, 1) (二) (-1,0) 号 O 0号 01 19 () (-²,-²) )。 at trafte 135°…

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Q: (b) Let x1(t) = cos (6tt) and x2(t) = sin(30nt). Determine whether the signal y(t) = x1(t) + x2(t)…

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Q: and as Use the chain rule to find sin(6) r = st, 0 = s + t3 dz as

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Q: S-) Find the general soluhon of sin'x y"-(25inx.cos x)y'+ Ccosx+1)y = Sih? x given that y-sihx and…

A: Please check step 2 for solution

Q: 5. DETAILS SCALCET9M 14.5.015. az az and as at Use the chain rule to find sin(8) Z = r = st, 0 = s3…

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Q: 4.1 z + cos(72) -dz, c z(z² +1) with C : |z – i| =.

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Q: Q2/provethate Cos17 +SinI7 cos17-Sın17 %3Dtun62

A: We have to prove that                               cos17°+sin17°cos17°-sin17°=tan62°

Q: 1. Use the Euler, improved Euler and Runge-kulta methods to Solve the folllowing ODE s: 4 2 y =0 y…

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Q: 3- If a y + sin y + arctan a = sin 1 then what is the value of at (0,1)? dz -2 b)- 1+ cos 1 -1 1 a)…

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Q: Given that the characteristic equation has the following roots, what is the complementary solution?…

A: We will find out the required complementary function.

Q: Example 1: Find length of the cardioid r = a(1 – cos 0) %3D | from 0 = 0,0 = 2n

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Q: QUESTION 5 Evaluate F dr, where F(x,y)=[2y-3cos(x)]i + [4x +6sin(y)]j and C goes counterclockwise…

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Q: 1. Find ar, aN, N, T, and k for: (a) F(t) = (5t, t, 4t) at the point (10, 4, 8) (b) ř(t) = (1 – 2t²,…

A: (b) Given rt→=<1-2t2,2-t2,t3> and given point is -1,1,-1. Therefore by comparing, we get…

Q: Given that the characteristic equation has the following roots, what is the complementary solution?…

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Q: 5. Suppose that u is a harmonic function in the disk D = {r< 2} and that u = sin 30 – 2 cos 30 + 4…

A: Given: The given harmonic function u=sin3θ-2 cos3θ+4 in the disk D=r≤2 for r=2.

Q: π 3n The number of solutions to cos 0 - < c, with 0 < c < 1 and

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Q: A standing wave on a 2-m stretched string is described by: y(x,t) = 0.1 sin(2rtx) cos(50tt), where x…

A: Solution :-

Q: 2. Draw the graph z = - cos(y) for 0 < y < 2n, and then use it to help you sketch solutions of y' =…

A: Firstly we draw the graph of z=-cos(y) for the given interval. Then we find the critical points and…

Q: Determine c, and c2 so that y(x) = c, sin 2x + c2 cos 2x + 1 will satisfy the conditions y () = 0…

A: Consider the function: yx=c1sin 2x+c2cos 2x+1. Calculate c1 and c2. Given yπ8=0 and y'π8=2.   Since…

Q: The value of 'b' for which u(x, y) = ebx cos 5y is harmonic

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Q: 1.Why does the following DE have an unique solution on an open rectangle that contains the point (O;…

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Q: The values of C, and C, so that y(x) = C, sin (2x) + C2 cos (2x) satisfies the following conditions:…

A: Solution:

Q: 4X^) Prove the reduction formula feese de n-2 cW Use part (a) to evaleate (cos2x dx Use parts (a)…

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Q: 1-Find the Cauchy principle value (showing details): J_co (7*+5x²+4)' cos(4x) dx 8.

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Q: V3 %3D 7) Give a general formula for all the solutions of cos 0

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Q: 2x Cos 23 find diy %3D

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Q: 4. Write u = -2 cos Tt – 3 sin at in the form u = Rcos(wot – 8).

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Q: 7. Find the length of the curve: r = 1 + cos 0

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Q: Determine cı and c2 so that y(x) = c1 sin 2x + c2 cos 2x + 1 will satisfy the conditions y () = 0…

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Q: 1) Find the fundamental period of the functionu +v, if any, by examining whether the functions u (t)…

A: All trigonometric functions are periodic. To find if ut=sin2t is periodic: Express it in terms of…

Q: Let y= c1 cos 2x +c2 sin2x be a two-parameter family of solutions of the second-order DE y"+4y=0.…

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Q: 1 (a) Calculate and fully simplify |a² cos(z) dz.

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Q: Find cos (0 + p) given that cos 0 = and cos p = and that 0 and p are %3D between 0 and n/2.

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Q: The auxiliary roots of the auxiliary equation associated with a certain HLDE are m=±3, ±3i, ± 3i.…

A: Solution is given as below:

Q: Given that 7(1 + h) – 7(1) = (h - 1 + cos(h), e" -e-", In(2h + 1)) for all h where -. a 7'(1 :…

A: We will use the definition of derivative to find r'(1) as shown below

Q: (a) Find first fundamental form of X(t,0) = (r(t) cos 0,r(t) sin 6, z(t)).

A: Note: As per bartleby instruction when more than one question is given only one has to be answered.…

Q: 2 tan-1(y). x In(xyz), q ƏV when x = y = % = 1. ду Let V = eP cos(qr), with p = z cos(TY) and r = By…

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Q: 22-j is 1. -1+jZ If Z = cos 0 + j(1+ sin 0), show that the magnitude of

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Q: 4e + 6x° + 9 cos z)dr %3D

A: Given

Q: e work of a particle moving counter-clockwise around the vertices (2,0), (-2,0) and -3) 3e* F…

A: Greens theorem is used