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Mathematics

Which of the following is the value of the sine of the angle shown above?

A.-√2/2
B.√2/2
C.45
D.315

答案和解析

答案：A

解析：

Choice A is correct. Recall that if θ is an angle measured counter-clockwise from the positive x-axis, the point, P, where the terminal ray of the angle intersects with the unit circle is P=(cosθ, sinθ).

To evaluate the sine and cosine, use a unit circle to see that the angle 7π/4 corresponds to the ordered pair (√2/2, -√2/2).

Since the y-coordinate of that ordered pair corresponds to the sine of that angle, then sin 7π/4 = -√2/2.