Practice with Partial Unit Circle

π/4 goes up from the x-axis... (one-quarter slice)

-π/6 goes down from the x-axis... (one-sixth slice)

 $\sin\left(\frac{\pi}{4}\right)=y\ =\ \frac{\sqrt{2}}{2}$  

 $\cos\left(\frac{\pi}{4}\right)=x=\frac{\sqrt{2}}{2}$  

 $\tan\left(\frac{\pi}{4}\right)=\ \frac{y}{x}=\frac{\sqrt{2}\div2}{\sqrt{2}\div2}=1$  

 $\sin\left(-\frac{\pi}{6}\right)=y\ =\ -\frac{1}{2}$  

 $\cos\left(-\frac{\pi}{6}\right)=x=\frac{\sqrt{3}}{2}$  

 $\tan\left(-\frac{\pi}{6}\right)=\ \frac{y}{x}=\frac{-1\div2}{\sqrt{3}\div2}=-\frac{1}{\sqrt{3}}$  

Cosecant is the flip of Sine $\left(\frac{\sqrt{2}}{2}\right)\longleftrightarrow\left(\frac{2}{\sqrt{2}}\right)$  

Secant is the flip of Cosine

Cotangent is the flip of Tangent