Question

How do you write in simplest radical form the coordinates of point A if A is on the terminal side of angle in standard position whose degree measure is `theta`: OA=15, `theta=135^circ`?

Answer 1

The coordinates are `(15/sqrt(2),15/sqrt(2))`

Explanation:

Start by making a reference triangle for your angle.

The inner angle of the right triangle is `180-135=45` degrees. The side opposite the `45` degree angle is the `y` coordinate, and the side adjacent to the `45` degree angle is the `x` coordinate.

The properties of a `45-45-90` right triangle are

So the hypotenuse is `15=ysqrt(2)`. We can solve this by dividing both sides by `sqrt(2)`.

`x=15/sqrt(2)` and `y=15/sqrt(2)`.

Thus, the coordinates are `(15/sqrt(2),15/sqrt(2))`