Sinusoids

Basic Cosine and Sine functions Let θ be a real valued angle measured in radians Since cos θ and sin θ are periodic with period equal to 2Π, for any positive or negative integer k, cosine function is symmetric, or more precisely, even-symmetric about the origin, while the sine function is anti-symmetric (or odd-symmetric): cos(-θ) = cos θ; sin(-θ) = -sin θ The sine function is obtained from the cosine by a delay in θ = Π/2 radians; the cosine is obtained from the sine by an advance in θ = Π/2

Addition of Sinusoids Adding two sinusoids of the same frequency but different amplitudes and/or phases yields another sinusoid with that frequency

Addition of Sinusoids Using trigonometric identities,        

Example Express x(t) = cos ω0t - √3 sin ω0t as a single sinusoid Sketch the phasor addition of the sinusoids Solve this problem using Matlab

Class Exercise Express x(t) =-3 cos ω0t + 4 sin ω0t as a single sinusoid Sketch the phasor addition of the sinusoids Solve this problem using Matlab