Question

Give the sin, cos, and tan for the point on the Unit Circle at 210°

Answer 1

It's important to know that the unit circle refers to a circle with a radius of 1 unit. As the image below shows.

As you can observe, in the graph, the angle 210° is placed on the third quadrant, where cosine and sine functions are negative tangent functions are positive.

$\begin{gathered} y=\cos (210)=-\cos 30=-\frac{\sqrt[]{3}}{2} \\ y=\sin (210)=-\sin 30=-\frac{1}{2} \end{gathered}$

Then, we divide the functions above to find the tangent

$\tan (210)=\frac{\sin(210)}{\cos(210)}=\frac{-\frac{1}{2}}{-\frac{\sqrt[]{3}}{2}}=\frac{1}{\sqrt[]{3}}\cdot\frac{\sqrt[]{3}}{\sqrt[]{3}}=\frac{\sqrt[]{3}}{3}$

Hence, the functions are

$\begin{gathered} \sin (210)=-\frac{1}{2} \\ \cos (210)=-\frac{\sqrt[]{3}}{2} \\ \tan (210)=\frac{\sqrt[]{3}}{3} \end{gathered}$