ticbol did an excellent job of explaining.
Here are my versions . . .
I'll assume the angle are between and .
Find the exact value of:
We want the angle whose sine is
You are expected to know that:
Sine is negative in quadrants 3 and 4.
So we have a reference angle of in quadrants 3 and 4.
Hence, the angles are: .
Inside, we have: .
Then we have: . . . . the angle whose cosine is
We know that: .
Cosine is negative in quadrants 2 and 3.
Therefore the angles are: .
Inside, we have: . . . . the angle whose sine is
We don't know the exact value of this angle,
. . but we know it comes from this triangle:
5 * | 4
* θ |
* - - - - - *
Since sine is negative in quadrants 3 and 4,
. . the two possible angles look like this:
-3 | | 3
- + - - - + - - - - - - - - - + - - - + -
: θ / | | \ θ :
-4: /5 | | 5\ :-4
: / | | \ :
* | | *
. . the answers are: .