Question

Find two negative and three positive angles, expressed in radians ,for which the point on the unit circle that corresponds to each angle is$\left(\frac{-\sqrt{2}}{2},\frac{\sqrt{2}}{2}\right)$.

Short answer

Two negative angles are$\cos t=\frac{-\sqrt{2}}{2},\tan t=-1$and positive angles are$\sin t=\frac{\sqrt{2}}{2},csct=\frac{2}{\sqrt{2}}$

Step-by-step solution

Step 1. Given information .

Consider the given points$\left(\frac{-\sqrt{2}}{2},\frac{\sqrt{2}}{2}\right)$.

Step 2. Finding negative and positive angles.

We follow the definition of six trigonometric function using $P=\left(\frac{-\sqrt{2}}{2},\frac{\sqrt{2}}{2}\right)=\left(x,y\right)$where $x=\frac{-\sqrt{2}}{2},y=\frac{\sqrt{2}}{2}$

$$\begin{gathered} \sin t=y=\frac{\sqrt{2}}{2},\cos t=x=\frac{-\sqrt{2}}{2},\tan t=\frac{y}{x}=-1 \\ csct=\frac{2}{\sqrt{2}},sect=\frac{-2}{\sqrt{2}} \end{gathered}$$