## anonymous 5 years ago Solve cos^(2)(x) - 3sin(x) = 3 for x on [0, 2pi] So I have simplified the function down to (-sin(x) - 2)(sin(x) + 1) = 0 or (-sin(x) -1)(sin(x) + 2) = 0 I have determined x = 3pi/2 as sin(3pi/2) = 1/2 Is that the only value possible As I don't think there is a value in the domain of this function that I could use to solve (sin(x) + 2) or (-sin(x) - 2) I could imput arcsin(2) but would that be wrong and if so why?

1. watchmath

because the value of sin is at most 1. SO arcsin(2) is undefined. So the solutions only comes from -sin x -1 =0

2. anonymous

sin(3pi/2) = -1

3. anonymous

made a typo. so I'm correct.

4. watchmath

yes $$e\pi/2$$ is the only answer

5. anonymous

so I should always adhere to the range of the unit circle when dealing with trig functions?

6. watchmath

I mean $$3\pi/2$$

7. anonymous

yeah I was wondering lol