Prove that 1+ cos theta + cos 2theta + .... cos ntheta = 1/2 + (sin(n+1/2)theta)/2sin(theta/2)

Expert Solution

Colby Messinger answered 1 year ago

(a) Solve the given equation. 2 cos2(theta) + sin(theta) =1

(a) Solve the given equation. 2 cos2(theta) + sin(theta) =1 theta= ____ (b) The measure of an angle in standard position is given. Find two positive angles and two negative angles that are coterminal with the given angle (Enter your answers in comma separated lists). -5pi/4 ____rad

Let x[n] = cos(17?n 64 ) + 2sin(23?n 32 ) for 0 ? n ? 255,...

Let x[n] = cos(17?n 64 ) + 2sin(23?n 32 ) for 0 ? n ? 255, and 0 otherwise. The signal x[n] is passed through an LTI system with transfer function H(z) = (1? 1 2z?1)(1? 1 3z?1). Denote the signal at the output of the system by y[n]. We want to recover x[n] by passing y[n] through an inverse system. (a) Find (analytically) an impulse response g[n] of the inverse system, G(z) = 1 H(z). (Note: the inverse system...

f (x) = -0.248226cos (2 x) - 0.0184829cos ((2+2)x) - 0.0594608cos(x)sin(x) + 0.123626*sin ((2+2)x). The intervall...

f (x) = -0.248226*cos (2 x) - 0.0184829*cos ((2+2)x) - 0.0594608*cos(x)*sin(x) + 0.123626*sin ((2+2)x). The intervall is ]0, 3/2[ What is the local maximum and local minimum? Answer with 5 decimals

a. (5 Marks) 1 1 cos(x)cos(y) = -cos(x-y) + -cos(x + y) 1 l sin(x)sin(y) =...

a. 1 1 cos(x)cos(y) = -cos(x-y) + -cos(x + y) 1 l sin(x)sin(y) = -cos(x-y)--cos(x+ y) 1 l sin(x)cos(y) =—sin(x-y) +-sin(x + y) A DSB-FC (double sideband-full carrier) signal s(t) is given by, s(t) = n cos(2rr/cf)+ cos(2«-/mt)cos(2«-fct) What is the numeric value for the AM index of modulation, m, fors(f) ?

An equation is given cos(theta/2) − 1 = 0 (a) Find all solutions of the equation.

An equation is given cos(theta/2) − 1 = 0 (a) Find all solutions of the equation.θ = (b) Find the solutions in the interval [0, 2π).θ =

What is the area inside the limacon r=1 + 2sin(theta) but outside of the inner loop?

Simplify. Do not give trig values. 1) 2 sin40 cos 40 2) 10 sin 18 cos...

Simplify. Do not give trig values. 1) 2 sin40 cos 40 2) 10 sin 18 cos 18 3) (tan 22)^2 4) 2 (cos 37)^2 - 1 5) (cos 29)^2 - 1 6) (sin 33)^2 + (cos 33)^2 7) (sin 38)^2 - (cos 38)^2 8) cos 67 cos 31 + sin 67 sin 31 9) cos 81 cos 53 - sin 81 sin 53 10) cos 46 / sin 46 11) sin 50 / cos 40 12) sin 44 cot 44...

Question

Prove that 1+ cos theta + cos 2theta + .... cos ntheta = 1/2 + (sin(n+1/2)theta)/2sin(theta/2)

Solutions

Expert Solution

Related Solutions