Answer: (sqrt(2)/2, -sqrt(2)/2)
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Step-by-step explanation:
The angle 315 degrees is in the interval 270 < theta < 360. This places the angle in quadrant 4.
To get the reference angle, we subtract from 360
360-315 = 45
So the reference angle is 45 degrees. Because we're in quadrant 4, we'll need to remember the following
cosine is positive in quadrant 4
sine is negative in quadrant 4
Since sin(45) = cos(45) = sqrt(2)/2 after using the unit circle, this means
cos(315) = sqrt(2)/2 and sin(315) = -sqrt(2)/2
The terminal point is located at (sqrt(2)/2, -sqrt(2)/2)
The cosine of the angle theta handles the x coordinate, while the y coordinate is handled by sine.