Determine the exact value of $\cos(-5\pi/4)$
I know:
$\cos(\theta)=x/1$,
$5\pi/4$ on the unit circle is $225^\circ$.
Therefore $\cos (225^\circ)=x/1$.
In order to find the exact value I need to find the reference angle.
Here is my first question:
- Do I use the angle $5\pi/4$ on the unit circle, equaling $225^\circ$
? - Or, since it is negative, assume that $-5\pi/4 = 3\pi/4$ (going
clockwise)?
I think I know where to go once I have the reference angle.
Any hints as to how I would find that?
EDIT:
So, if $-5\pi/4 = 3\pi/4$, and $3\pi/4 = 135^{\circ}$
The reference angle is $45^{\circ}$
$cos(45^{\circ}) = 1/\sqrt 2$
$\cos$ is negative in quadrant II
$= 1/{-\sqrt{2}}$
How does that look?
Best Answer
Use the second one. Negative means you go backwards (clockwise) so -5π/4 would be 3π/4.
After edit: That seems right :)