Agohofidov6

## Answered question

2021-12-26

How do you find the terminal point on the unit circle determined by $t=5\frac{\pi }{12}$ ?

### Answer & Explanation

lovagwb

Beginner2021-12-27Added 50 answers

Explanation:
The arc is $t=\frac{5\pi }{12}$
x-cordinate is : $x=\mathrm{cos}\left(\frac{5\pi }{12}\right)$
y-coordinate: $y=\mathrm{sin}\left(\frac{5\pi }{12}\right)$
Calculator gives $x=\mathrm{sin}\left(\frac{5\pi }{12}\right)=\mathrm{sin}75=0.97$
and $y=\mathrm{cos}75=0.26$

jean2098

Beginner2021-12-28Added 38 answers

The terminal point on the unit circle has the cosine as x-coordinated and the sine as y-coordinate.

In this case $\theta =\frac{5\pi }{12}$
$\left(\mathrm{cos}\frac{5\pi }{12},\mathrm{sin}\frac{5\pi }{12}\right)$
As $\theta =\frac{5\pi }{12}$ is not one of the special angles, we will use a calcutator to evaluate the cousine and the sine at $\theta =\frac{5\pi }{12}$.
$\mathrm{cos}\frac{5\pi }{12}={\mathrm{cos}75}^{\circ }\approx 0.2588$
$\mathrm{sin}\frac{5\pi }{12}={\mathrm{sin}75}^{\circ }\approx 0.9659$
Thus the coordinates of the terminal point at $\theta =\frac{5\pi }{12}$ are then:
$\left(\mathrm{cos}\frac{5\pi }{12},\mathrm{sin}\frac{5\pi }{12}\right)=\left(0.2588,0.9659\right)$

nick1337

Expert2022-01-08Added 777 answers

Maybe this will help me, thanks

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