Question

The point (1, −1) is on the terminal side of angle θ, in standard position. What are the values of sine, cosine, and tangent of θ? Make sure to show all work.

Answer 1

notice the picture below

x = 1 and y = -1

now... recall your SOH CAH TOA   $\bf sin(\theta)=\cfrac{y}{r} \qquad % cosine cos(\theta)=\cfrac{x}{r} \qquad % tangent tan(\theta)=\cfrac{y}{x}$

now.. what's the value for "r" or the radius? well, using the pythagorean theorem $\bf c^2=a^2+b^2\implies c=\sqrt{a^2+b^2}\qquad \begin{cases} a=x\\ b=y\\ c=r \end{cases}$