Question

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 1

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°

Answer 2

Answer:

0.38π

Step-by-step explanation

if you´re using edmentum/plato I am 100% sure this is the correct answer becusae I looked at the coding. However I do not feel confident enough in explaining how to get this answer but you have to use:

quotent identity: tan(∅)= sin(∅)/cos(∅)

Then you have to solve 2 quotent identities

$tan(theta)=\frac{\frac{5}{a} }{\frac{2}{a} } = \frac{5}{2} \\\\tan(theta)= \frac{sin(theta)}{cos(theta)\\\\ }$

After those steps Im not sure what to do but I know the answer is  0.38π I hopw this helps move you along to figure out the problem