Question

Trig helppp

Answer 1

Part I:
Would my answers be theta = 3pi/4 and theta = 7pi/4 ?

Answer 2

`Part I:`
`Would my answers be theta = 3pi/4 and theta = 7pi/4 ?`
yes that's correct

Answer 3

Awesome! For Part II, I got:
3pi/4 + 2npi and 7pi/4 + 2npi
Yeah?

Answer 4

while that is correct, there is a simpler way to condense those two general solutions

you can write them both as
x = 3pi/4 + pi*n
where n is any integer

Answer 5

notice if n = 1, then
x = 3pi/4 + pi*n
x = 3pi/4 + pi*1
x = 3pi/4 + pi
x = 3pi/4 + 4pi/4
x = 7pi/4

Answer 6

Oh that makes sense... how would I recognize to condense it?

Answer 7

It's just something you practice over and over til you get good at recognizing the different forms. I guess you could ask yourself: is one solution based off another? If so, then how?

In this case, 7pi/4 is one half-turn from 3pi/4, which is why you add on pi. To get the next solution, you add on another pi, and so on. Which is why the `pi*n` portion is there.

Answer 8

But 3pi/4 + 2npi and 7pi/4 + 2npi works fine just as well

Answer 9

Awesome, thanks! That makes a lot of sense :)

Answer 10

I'm glad I could help