Question

Use eulers equation to derive expansions for cos(a)sin(b) and cos(a)cos(b)

Answer #1

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Use eulers equation to derive expansions for cos(a)sin(b) and
cos(a)cos(b)

Derive the Laplace transform for the following time
functions:
a. sin ωt u(t)
b. cos ωt u(t)

Solve the given equation
2 cos^2 theta+sin theta =1
cos theta cos 20 + sin theta sin 20= 1/2

Solve for −?≤?≤?.
(a) cos x – sin x = 1
(b) sin 4x – sin 2x=0
(c) cos x−√3sin ? = 1

Derive the Laplace transform of the following time domain
functions
A) 12 B) 3t sin(5t) u(t) C) 2t^2 cos(3t) u(t) D) 2e^-5t
sin(5t)
E) 8e^-3t cos(4t) F) (cost)&(t-pi/4)

y = (6 +cos(x))^x
Use Logarithmic Differentiation to find dy/dx
dy/dx =
Type sin(x) for sin(x)sin(x) ,
cos(x) for cos(x)cos(x), and so on.
Use x^2 to square x, x^3 to cube
x, and so on.
Use ( sin(x) )^2 to square sin(x).
Use ln( ) for the natural logarithm.

If u(t) = sin(6t), cos(2t), t and v(t) = t, cos(2t), sin(6t) ,
use Formula 4 of this theorem to find d dt u(t) · v(t) .

Verify that the functions y1 = cos x − cos 2x and y2 = sin x −
cos 2x both satisfy the differential equation y′′ + y = 3 cos
2x.

Solve
sin(5x)cos(9x)−cos(5x)sin(9x)=−0.45sin(5x)cos(9x)-cos(5x)sin(9x)=-0.45
for the smallest positive solution.

Find the exact value of the expressions cos(a+b), sin(a+b) and
tan(a+b) under the following conditions:
cos(x)=12/13,x lies in quadrant 4, and sin(y)=-4/11, y lies in
quadrant 3
a. cos (a+b) b.sin(a+b) c.tan(a+b)

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