Question

pi/3 is the reference angle for: A. 2pi/3 B. 15pi/3 C. 7pi/3 D. 19pi/3 **its CHOOSE ALL THAT APPLY!!!:) my answers: C. 7pi/3 and D. 19pi/3 are those right??

Answer 1

Answer:

yes those are right but 2pi/3 is also right.

Step-by-step explanation:

Answer 2

Answer:

The correct answers are A,C and D

Step-by-step explanation:

Given an angle θ, we call the reference angle for θ as '' θ ref ''.

Using the x-axis as our frame of reference, θ ref is always the smallest angle that you can make from the terminal side of an angle with the x-axis.

Let's note the quadrants of the IR2 as Q.

For an angle θ in QI, θ ref = θ

For an angle θ in QII, θ ref = π - θ

For an angle θ in QIII, θ ref = θ - π

For an angle θ in QIV, θ ref = 2π - θ

For A. $\frac{2\pi }{3}$

This angle is in QII ⇒ θ ref = π - θ

                                   θ ref = π - $\frac{2\pi }{3}$ = $\frac{\pi}{3}$

For B. $\frac{15\pi}{3}$

This angle is equal to $\frac{15\pi }{3}-4\pi =\pi$

This angle is in QII ⇒ θ ref = π - θ

                                   θ ref = π - π = 0

For C. $\frac{7\pi }{3}$

This angle is equal to $\frac{7\pi }{3}-2\pi=\frac{\pi}{3}$

This angle is in QI ⇒ θ ref = θ = $\frac{\pi }{3}$

For D. $\frac{19\pi }{3}$

This angle is equal to $\frac{19\pi }{3}-6\pi=\frac{\pi }{3}$

This angle is in QI ⇒ θ ref = θ = $\frac{\pi }{3}$

The correct answers are A,C and D.

Notice that in the angles bigger than 2π we subtract multiples of 2π to know in which quadrants are the angles.