Given x sin4t, y = -cos4t, then find at t =.

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A: We will use the fact that  sin(x+y)=sinx cosy +cosx siny to evaluate the given integral.

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

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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: Given that sin t = 1/2 and 0 ≤ t < π/ 2, find the value of cos t using a trigonometric identity.

A: Given

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Q: Compute -i + cos -i sin a - sin a + i cos a where a E (T, ).

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Q: If z = x?y + 3xy, where x = sin 2t and y = cos t, find dzidt when t = 0.

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Q: Given that y = sin (t) and x cos²(4t*), hence find dx dy

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Q: Find  dy/dx, given ? = sin √x

A: Chain rule in differentiation: also,

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

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Q: Find sin t and cos t for the given value of t. t = 150°

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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: In AXYZ, the measure of ZZ=90°, XZ = 63, ZY = 16, and YX 65. What ratio represents the sine of ZX?

A: Given that right triangle XYZin which XZ=65 , ZY=16 and XY=65we have to find sin∠X

Q: The value C in y = sin (Bx +C) is called the _________.

A: The given equation is y=sinBx+C

Q: Given sin t =2/3and cos t =√5/3, find the value of each of the four remaining trigonometric…

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Q: Evaluate ∫ a cos x dx and ∫ a sin x dx, where a is a constant.

A: Given∫a cos x dx

Q: Eliminate parameters A and B but not parameter C by differentiating x with respect to t. x=A sin…

A: The given equation is: x=Asin(Ct+B)

Q: A certain substitution gives S sin³ x cos" x dx = S(u7 – u5) du. What is n?

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Q: 1. Given the equation sin(y) + cos(r) = 2, find

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Q: If y = cos(sin(2.x)), find . dx

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Q: only 8 please

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Q: Given the equation 5 sin 6xy = 3, evaluate dy Assume that the equation implicitly defines y as a…

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Q: Use the formula for the slope of the tangent line to find of c(0) = (sin(20), cos(70)) at the point…

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Q: The position of an object attached to a spring is given by s (t) = cos(4t) — —sin(4t), - where t is…

A: The position of an object,st=14cos4t-16sin4t on the interval 0<t<3

Q: If y = sin (m sinhx), find the value of (yn)o

A: Given that,  Differentiate w.r.t.                         . . .(on squaring both sides)…

Q: a)- Find for, (x+ y)* = tan-14× + T* + InIny dy dx

A: To find dy/dx.

Q: Given y = cos(3x), find O O 3 2- * N O √3 3√3 dy at x = 5

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Q: Demonstrate and derive the following Bernoulli's Equation. - 2y tan x = y² tan²x dx

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Q: If  sin⁡x=e^y,  0<x<π, what is dydx in terms of  x?

A: Given sin x = ey   ..................(1) Differentiating both sides with respect to x  d(sinx) / dx…

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

A: This question is related to vector calculus

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: Find of the following functions. [ dr (a) y = sec(7?) (b)y = sin7x + cos5a

A: here we can find the derivative as below.

Q: Solve the following Riccati equation dy _2 cos? x – sin² x + y² 2 cos x y1(x) = sin x dx

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Q: Given that (-) x sin-1 -1 = COS eya. dy in the terms of x and y. dx Find

A: Given: xsin−1⁡1y=cos−1⁡eyx Since, dsin-1xdx=11-x2 and dcos-1xdx=-11-x2

Q: When x³ cos(x?) dx is evaluated using IBP, the value of v du is? ...

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Q: In AXYZ, the measure of ZZ=90°, XZ = 63, ZY = 16, and YX = 65. What ratio represents the sine of X?

A: First sketch a triangle for the given measures as shown below.

Q: Given: X = 4 cos 20 and y = 2 sin 20 What is the value of d y dx? in terms of

A: We have to solve

Q: sketch r= la 2 Sin'co+)

A: r=1-2sin2(θ+π3)

Q: Given: x = 4 cos 26 and y= 2 sin 26 What is the value of in terms of 6. dz O dy csc 29 dx2 -csc 20 O…

A: The solution is given below:

Q: implicitly, if e*(e» – 1) + sin(2x + 5y) = In(v7) – · cot(2x) 8. Find %3D y+2

A: Given,

Q: Given cos x sin x < 0; tan y = sec y < 0, find sin(x+y)

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Q: Given: = 0 – sin 0; y=1– cose Find: dz2

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Q: Given x = sin4t, y = -cos4t, then find at %3D t = 16 dx О a.3 O b. 2 O c.0 O d. 1

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Q: (b) If y = sin (m sinhx), find the value of (yn)o ·

A: Given   it has to find nth derivative at .

Q: If V) AT sin (2 Tf t)/(2 TfT), find the energy contained in v (t).

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Q: find dr/dθ r = θ sin θ + cos θ

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Q: Let f (t) = et sin 5t

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Q: (b) If y = sin (m sinh¯x), find the value of (yn)o ·

A: Hi, you may find the answer in the form of hand-written note.