1. Sinusoids

2. 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

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

4. Addition of Sinusoids
Using trigonometric identities,        

5. 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

6. 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