Check all that apply. (pi/3) is the reference angle for: 1. 15pi/3

2. 2pi/3

3. 7pi/3

4. 19pi/3

2π/3, 7π/3 and 19π/3 are the reference angles.

Step-by-step explanation:

Given the angle π/3, the reference angle to this angle is the angle similar to the given angle.

The angle similar to the angle is derived by adding 2πk to each resulting angle where k is integers from 1 and above

Given initial angle of π/3

The following are the reference angles:

When k = 1

theta(k) = π/3 + 2πk

theta(1) = π/3 + 2π(1)

=(π+6π)/3

= 7π/3

When k = 2

theta(2) = π/3 + 2π(2)

= π/3 + 4π

=(π+12π)/3

= 13π/3

When k = 3

theta(2) = π/3 + 2π(3)

= π/3 + 6π

=(π+18π)/3

= 19π/3

Note that π-theta is also a reference angle where theta us the given angle.

π-theta= π-π/3

= 3π-π/3

= 2π/3

From the calculation above, 2π/3, 7π/3 and 19π/3 are the reference angles.

answer:

sometimes

*i think