# Evaluating $\sin15^\circ$ using Definition 2 of Trigonometric Functions

I am studying trigonometry from Cynthia Young's book(it is a long book).
I have studied the Definition 2 of trigonometric functions(The Cartesian Plane) but not the Definition 3(Unit Circle Approach).
Using the Definition $2$,I can very easily calculate the trig. functions of $30°,45°,60°,120°,135°,150°,210°,225°,240°,300°,315°$ and $330°$ because $30-60-90$ triangles and $45-45-90$ triangles are special triangles. But if i try to calculate $\sin 15°$ using Definition 2 of trig. functions,I'm unable to.
But there must be a way of doing this. So,my question is that-A $15°$ angle has been drawn on the cartesian plane.It passes through a point whose x-coordinate is $2$. What is the $y$-coordinate of that point?
Because after knowing this,I'd easily be able to calculate $\sin 15°$ using $\sin\theta=\frac{y}{r}$

## 1 Answer

use that $$\sin(30^{\circ})=2\sin(15^{\circ})\cos(15^{\circ})$$ and $$\cos^2(x)+\sin^2(x)=1$$