1. ## Quick question about sum and difference formula

I just need help on #3.

To find the Φ of the equation wouldn't we do tan Φ = a2/a1? If so how come the answer in the back of the book says sqr2 sin(t +3pi/4).

When I did the tan Φ = a2/a1 = -1/1 I would get a Φ angle of -0.78539.

Please confirm if I did something wrong or the book is wrong. Thank you!

2. The given problem can be written as
sqrt(2)[sint*-sqrt(1/2) + cos(t)*sqrt(1/2)]....(1)
Now sin(3π/4) = sqrt(1/2)
and cos(3π/4) = -sqrt(1/2)
Substitute these values in eq.(1) and see what you get.

3. 1) Why are you using your calculator when an exact value is requested?

2) I'm not really sure how to help you except to provide examples of how to proceed. Usually, just try somehthing that seems to make sense and revise as necessary. Example below:

For #3, I tried $\sin\left(t - \frac{\pi}{4}\right)$ - Nope, not quite right. Sign is wrong.

Then, I tried $\sin\left(t - \frac{5\pi}{4}\right)$ - Nope, not quite right. Amplitude is wrong.

Finally, I tried $\sqrt{2}\cdot\sin\left(t - \frac{5\pi}{4}\right)$ - That's better.