Question

Which is the radian measure for 315° and its associated coordinate point on the unit circle?

A) seven fourths pi; negative square root 2 over 2 comma square root 2 over 2

B) three fourths pi; square root 2 over 2 comma negative square root 2 over 2

C) seven fourths pi; square root 2 over 2 comma negative square root 2 over 2

D) three fourths pi; negative square root 2 over 2 comma square root 2 over 2

Answer 1

The radian measure for 315° is 7/4π and its associated coordinate point on the unit circle is (−√2/2, √2/2).

Step-by-step explanation:

The radian measure for 315° is 7/4π and its associated coordinate point on the unit circle is (−√2/2, √2/2).

To convert degrees to radians, we use the formula:
Radian measure = (Degree measure x π) / 180
So, for 315°:
Radian measure = (315 x π) / 180
Radian measure = (7/4π)

On the unit circle, the point associated with 315° is obtained by taking the cosine of the angle as the x-coordinate and the sine of the angle as the y-coordinate. The cosine of 315° is -√2/2 and the sine of 315° is √2/2. Therefore, the coordinate point is (−√2/2, √2/2).