Exercises: Sine, Cosine and Tangent on the unit circle

$\cos \left(\gamma \right)=-\sin \left(\gamma \right)$

The angle(s) must be in the second and fourth quadrants.

$\sin \left(\gamma \right)=\cos \left(\gamma \right)$ holds if $\gamma ={45}^{\circ }$. However, the presign of sine and cosine are still the same.

To this angle $\gamma ={45}^{\circ }$ , the corresponding angles in the other quadrants with opposite presigns are are

1st angle

$\gamma ={135}^{\circ }$

$-\left(\frac{\sqrt{2}}{2}\right)=-\frac{\sqrt{2}}{2}$

2nd angle

$\gamma ={315}^{\circ }$

$-(-\frac{\sqrt{2}}{2})=\frac{\sqrt{2}}{2}$

$\frac{\sqrt{2}}{2}=\frac{\sqrt{2}}{2}$