To rewrite y (t) = 2sin4πt + 5cos4πt in the form Asin (ωt+Φ), solve for Φ. Show your work and solution in the response box.

Answer: ¢=68.2

Step-by-step explanation:

y (t) = 2sin4πt + 5cos4πt

Let, x = Asin¢ = 5

y = Acos¢ = 2

A = sqrt (5²+2²)

A = 5.39

y (t) = Acos¢sin4πt + Asin¢cos4πt

From Trigonometry rule,

y (t) = Asin (wt + ¢)

tan¢ = 5/2

¢ = arctan (5/2) = 68.2°

y (t) = 5.39sin (wt + 68.2)

Where w = 4π

The angle ¢ = 68.2°