Question

Find the Reference Angle -(3pi)/5

Answer 1

To find the reference angle for -(3pi)/5, we add pi to it, yielding (2pi/5), which is the positive acute angle that the terminal side of the angle makes with the x-axis.

Step-by-step explanation:

The student asked to find the reference angle for -(3pi)/5. In trigonometry, the reference angle is the positive acute angle made with the x-axis by the terminal side of the given angle when measured in standard position.

Given the angle -(3pi)/5, which is in the third quadrant when drawn in standard position, we can find its reference angle by adding pi to it, as angles in the third quadrant have a reference angle that is their angle plus pi.

Here's the step-by-step:

1. Since -(3pi)/5 is negative, it implies a rotation clockwise from the positive x-axis.
2. The reference angle is the smallest positive angle that the terminal side makes with the x-axis. For angles in the third quadrant, which is where our angle lies, we add pi to obtain a positive counterpart.
3. Therefore, to find the reference angle for -(3pi)/5, we compute (pi) - |-(3pi)/5| = (5pi/5) - (3pi/5) = (2pi/5).
4. The reference angle is (2pi/5).