Question

Find the measure of a negative angle coterminal with 3π/4.

A) -π/4
B) -π/2
C) -π
D) -3π/4

Answer 1

To find the negative angle coterminal with 3π/4, we subtract 2π and add it back until we get an angle in the range of one full circle, resulting in -5π/4, which simplifies to -3π/4. Thus, the correct answer is D) -3π/4.

Step-by-step explanation:

To find the measure of a negative angle coterminal with 3π/4, we need to subtract 2π from 3π/4 because coterminal angles are separated by integer multiples of 2π radians (or 360° in degree measure). To find such an angle, which will be negative, we subtract 2π from 3π/4 as follows:

3π/4 - 2π = 3π/4 - 8π/4 = -5π/4

However, we want the angle that is within one revolution of the circle, so we add 2π to -5π/4 to find the corresponding negative coterminal angle:

-5π/4 + 2π = -5π/4 + 8π/4 = 3π/4

This simplifies to:

-5π/4 + 8π/4 = 3π/4

This indicates that the negative coterminal angle is -3π/4, which corresponds to answer choice D).