Question

How do you find the terminal point $p(x,y)$ on the unit circle determined by the given value of $t=-\frac{3\mathrm{\pi }}{4}$ ?

Answer 1

Determine the terminal point $\mathit{p}\mathbf{(}\mathit{x}\mathbf{,}\mathbf{}\mathit{y}\mathbf{)}$ on the unit circle.

Here, the circle is a unit circle.

So, the radius of the circle is $1$

The terminal point $p$ at $t$ is $\left(1·\cos t,1·\sin t\right)=\left(\cos t,\sin t\right)$.

The $y-$coordinate of this terminal point is always equal to the sine of the angle, and the $x-$coordinate of this terminal point is always equal to the cosine of the angle.

$\left(\cos \left(-\frac{3\mathrm{\pi }}{4}\right),\sin \left(-\frac{3\mathrm{\pi }}{4}\right)\right)=\left(-\frac{\sqrt{2}}{2},-\frac{\sqrt{2}}{2}\right)$

Hence, the terminal point $\mathit{p}\mathbf{(}\mathit{x}\mathbf{,}\mathbf{}\mathit{y}\mathbf{)}$ on the unit circle is $\left(-\frac{\sqrt{2}}{2},-\frac{\sqrt{2}}{2}\right)$.