Question

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?

Answer 1

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

Answer 2

sin(3pi/2) = -1

Answer 3

made a typo. so I'm correct.

Answer 4

yes \(e\pi/2\) is the only answer

Answer 5

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

Answer 6

I mean \(3\pi/2\)

Answer 7

yeah I was wondering lol