Question 4.2.3: Finding Values of the Trigonometric Functions at t = π/4 Fin...

The point P on the unit circle that corresponds to t=\frac{\pi}{4} has coordinates \left(\frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2}\right). We use x=\frac{\sqrt{2}}{2} and y=\frac{\sqrt{2}}{2} to find the values of the three trigonometric functions at \frac{\pi}{4}.

\sin \frac{\pi}{4}=y=\frac{\sqrt{2}}{2} \quad \cos \frac{\pi}{4}=x=\frac{\sqrt{2}}{2} \quad \tan \frac{\pi}{4}=\frac{y}{x}=\frac{\frac{\sqrt{2}}{2}}{\frac{\sqrt{2}}{2}}=1