Find the angle 0 between T and such that sin(0) = 2 V3 - 2

Q: With the aid of residues, and a carefully chosen contour, show that d.x x5 +1 5 sin(T/5)

A: We we solve the general form of the integral for n instead of 5 Then we will substitute n=5 in order…

Q: e (a cos bx + b sin bx) a + b? ax Secos bx dx=-

A:

Q: Find the quadrant in which the terminal point detemined by t lies. sin(t)<0 and cos(t)<0…

A:

Q: Find the speed at the given value of t. r(t) = (sin(3t), cos(6t), cos(7t)), t = " 2. II

A:

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

A: To evaluate the given definite integrals.

Q: Find the speed at the given value of t. r(t) = (sin(3t), cos(6t), cos(7t)), t = %3D (플) = 프2

A: Given:

Q: Find the length of the astroid x = cos3 t, y = sin3 t, 0 ≤ t ≤ 2π.

A:

Q: x = 1+ cos t, y = sin² t

A: on computing the derivative of the given curves with respect to t than we will find the dy/dt so

Q: Find the general solution of the equation. xsin ydx+ xcos ydy +2 sin ydx =0

A: The solution are next step

Q: If u(t) = (sin(2t), cos(2t), t) and v(t) = (t, cos(2t), sin(2t)), use Formula 5 of this theorem to…

A:

Q: 4r2-8)3/2 dz

A:

Q: 5 sin?(t) cos“(t) dt

A: ∫0π5 sin2t cos4t  dt=5∫0πsin2t. cos2t .cos2t dt=5∫0π sin2t ×1sin2t cos2t dt=5∫0πcos2t…

Q: Determine the values of A, B and C. 2 X²V4 – x²dx = A sin? t cos²t dt B

A: Consider the integration as I=∫02x24-x2dx Put  x= 2 sint⇒2 cos t dt =dx Also  x→0⇒t→0Againx→2⇒t→π2

Q: Eliminate the parameter t in the following. x = cos 2t, y = sin t

A: Given that x = cos 2t; y = sin t To eliminate: the variable t Needed formulae: cos 2t = cos2t -…

Q: Suppose the position function of a particle is given r(t) = (√3 cos (t), t-4, √3 sin(t)). If the…

A: Given : r(t)=3cos(t), t-4, 3sin(t) is the position function of a particle. To find : If the particle…

Q: Given: x = 0 – sin 0; y= 1 – cos 0 d'y Find: da?

A:

Q: J, sin a sin? cos" ,dx COS 2 2 2.

A:

Q: (e² sin*(2r)' 21² +1 , y = In

A: Use the lograthim rule of derivative and than with the help of chain rule calculate the derivative…

Q: find the speed at the given value of t. r(t) = (sin 3t, cos 4t, cos 5t), t =

A: Given: rt=sin3t, cos4t, cos5t To find the speed at the given value of t=π2. Solution: Speed is the…

Q: Calculate the length of the path over the given interval. (sin 4t, cos 4t), 0 <t <T

A:

Q: : Find the length of the cardioid r = 1 + cos 0 0 < 0 <T

A:

Q: Find the velocity, acceleration, and speed of a particle with the given position function. r(t) = (4…

A: Given position function isrt=4 cos t , 6t , 4 sin tWe have to find velocity , speed &amp;…

Q: Find the length of the path over the given interval. (2 cost − cos 2t, 2 sin t − sin 2t), 0 ≤ t ≤…

A: x(t)=2 cost − cos 2t y(t)= 2 sin t − sin 2t interval- 0 ≤ t ≤ π/2

Q: Rewrite f(x) = 5 sin(3x) – 2cos (3x) in the form A sin (Bx + C). Round your final angle to two…

A:

Q: Find the domain and range of each fuction f(x)=V sin x– cos x -

A: f(x) =sinx-cosx The number inside the radical must be greater than or equal to 0.    sinx-cosx≥0…

Q: find an appropriate trigonometric substitution of the form x=f(t)x=f(t) to simplify the integral…

A: Here, we use the substitution x=(sect)^2, as we know sec^2t=1+tan^2t, so x^2-1=tan^2t

Q: Using the substitution u = cos(2x), S sin (2x) cos (2x) dx %3D

A: The given integral is ∫sin52xcos32xdx.

Q: y(1) = yo + A cos(@t + p)

A:

Q: Photo attached

A: Given:

Q: (a) , f(r cos 0,r sin 0 )rdrde

A: Answer and explanation is given below

Q: Find the value of dʻy/dx at the point defined by the given value of t. x = 5 sin t, y = 5 cos t, t=…

A:

Q: Solve for t, 0 < t < 2π 14 sin(t)cos (t) = 8 sin(t) t = 0.96,5.32 Give your answers accurate to at…

A:

Q: 2 f(t) = ( tv4t2 + 1, sin(t) cos² (t), t2 + 1

A: As you ask parts b and c. in part b we need to find the equation of the tangent line to the curve at…

Q: Given F = cos t î + 7 sin t j + t²k, find

A: This question is related to vector calculus

Q: Find all intersection points between r = –sin 0 and r = v = V3 cos e.

A:

Q: Given x = sin3t, y = -cos3t, then find at t =. %3D dx а. 1 b. 3 с. О d. 2

A: We need to find dy/dx.

Q: dx 5) prove that sin x+c using method of trigonometric substitution. %3D

A:

Q: (3 cos t – 1)i + (2 sin t + 3)j,

A: We sketch the curve as

Q: Photo attached

A: The parametric equations is given by,

Q: (2 cos t, 2 sin t, t), where 0 <t < .

A:

Q: 2Tt Prove that a" sinax cos bx dx = 0 0.

A:

Q: A particle moves according to the position function s (t) = e2t sin (3t). %3D

A: Definition used -                        v(t)= dsdt                       a(t)=dvdt=d2sdt2…

Q: c(t) = (sin 2t, sin t), 0<t < n.

A: Solution Given c(t)=(sin2t,sint),0&lt;t&lt;πUsing Green's Theorem , calculate the area of the region…

Q: 22. Find the value of arcsine ( 2x + y ) given that TT sin-( 4x + 3y ) = 2 cos ( x + y ) = . TT and…

A:

Q: At what point does the sine function y = sin x, cross the y axis? O (T, O) O (0,0) O (1,0) O (0,1)

A: Given  function is y=sinx. We have to find the point at which the function y=sinx cross the y-axis.…

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

A:

Q: If sin t 2 and t is in the 3rd quadrant, - then cos t = Vī6 V34 5 Vī6 3 Vī6 | Vī6 3

A: Given Sin t=-(3/5) t =is in the 3rd quadrant Find out  cos t=?

Q: 2 cos e de 2 V1 – sin 0

A:

Q: Find a function u(r, 8) that is harmonic outside the unit disk, equals f(0) = 2 sin(30) + 4 cos (50)…

A: note : As per our company guidelines we are supposed to answer ?️only the first question. Kindly…