an angle with the radian measure of 9pi/5. find radian measure of its reference angle. answers: -4/5, 4pi/5, -pi/5, or pi/5

9π/5 = 2π + π/5

so the "angle in standard position" or the "reference angle"is π/5

To find the radian measure of the reference angle, you can subtract the given angle from 2π (or 360 degrees).

Given angle = 9π/5

Reference angle = 2π - (9π/5)

To subtract fractions with different denominators, we need to find a common denominator. In this case, the common denominator is 5:

Reference angle = (10π/5) - (9π/5)

Reference angle = π/5

Therefore, the radian measure of the reference angle is π/5.

To find the reference angle for an angle given in radians, you can perform the following steps:

Step 1: Subtract 2π (or multiples of 2π) from the given angle until you obtain an angle between 0 and 2π.

In this case, the given angle is 9π/5. To convert it to an angle between 0 and 2π, you can subtract 2π from it. By doing so:

9π/5 - 2π = (9π - 10π)/5 = -π/5

We now have a negative value, but we want an angle between 0 and 2π. Therefore, we add 2π to it:

-π/5 + 2π = (10π - π)/5 = 9π/5

Step 2: Take the absolute value of the angle obtained in Step 1.

In this case, the absolute value of 9π/5 is still 9π/5.

Therefore, the radian measure of the reference angle for an angle with the radian measure of 9π/5 is 9π/5.

None of the provided options (-4/5, 4π/5, -π/5, or π/5) matches the correct answer.