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The measure of angle θ is 7π/4 . The measure of its reference angle is _°, and tan θ is _.

A. 45°; 1
B. 90°; 0
C. 45°; -1
D. 180°; 1

1 Answer

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Final answer:

The reference angle of 7π/4 is 45°, and tan 7π/4 is -1. The correct answer is option C.

Step-by-step explanation:

The measure of angle θ is 7π/4. The measure of its reference angle is 45°, and tan θ is -1.

To find the reference angle of an angle in radians, we need to determine the positive acute angle that the terminal side of θ makes with the x-axis.

The angle 7π/4 is located in the fourth quadrant, where the reference angle is the difference between the angle and 2π radians (or 360° in degrees). Subtracting 7π/4 from 2π, we get π/4, which is equivalent to 45°.

The tangent of an angle in the fourth quadrant is negative, and since tan π/4 is 1, tan 7π/4 must be -1. Therefore, the correct answer is C. 45°; -1.

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