Question

hello can you help me with this trigonometry question in the question give the exact value and no decimals

Answer 1

We have the following:

The coordinates of the terminal point would be:

$\begin{gathered} x=\cos (\frac{5\pi}{4}) \\ y=\sin (\frac{5\pi}{4}) \end{gathered}$

now, for x:

$\begin{gathered} x=\cos (\frac{5\pi}{4})=\cos (5\cdot\frac{\pi}{4}\cdot\frac{180}{\pi})=\cos (225\degree)=-\frac{\sqrt[]{2}}{2} \\ \end{gathered}$

for y:

$y=\sin (\frac{5\pi}{4})=\sin (5\cdot\frac{\pi}{4}\cdot\frac{180}{\pi})=\sin (225\degree)=-\frac{\sqrt[]{2}}{2}$

The terminal point is:

$(-\frac{\sqrt[]{2}}{2},-\frac{\sqrt[]{2}}{2})$