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 thetaθ: OA=15, theta=135^circθ=135?

1 Answer
Nov 17, 2017

The coordinates are (15/sqrt(2),15/sqrt(2))(152,152)

Explanation:

Start by making a reference triangle for your angle.

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The inner angle of the right triangle is 180-135=45180135=45 degrees. The side opposite the 4545 degree angle is the yy coordinate, and the side adjacent to the 4545 degree angle is the xx coordinate.

The properties of a 45-45-90454590 right triangle are

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So the hypotenuse is 15=ysqrt(2)15=y2. We can solve this by dividing both sides by sqrt(2)2.

x=15/sqrt(2)x=152 and y=15/sqrt(2)y=152.

Thus, the coordinates are (15/sqrt(2),15/sqrt(2))(152,152)