Answer:
The reference angle is [tex]\frac{\pi}{3}[/tex]
Step-by-step explanation:
The given angle is [tex]t=-\frac{5\pi}{3}[/tex]
The reference angle is the acute angle, that a given angle makes with the x-axis.
First let us make a sketch of the given angle. See diagram in attachment.
Let [tex]\theta[/tex] be the reference angle of [tex]t=-\frac{5\pi}{3}[/tex]
Then, from the diagram, we need to subtract [tex]\theta[/tex] from [tex]-\frac{5\pi}{3}[/tex] to get to [tex]-2\pi[/tex].
We can therefore write the following equation and solve for [tex]\theta[/tex].
[tex]\Rightarrow -\frac{5\pi}{3}-\theta=-2\pi[/tex]
We group like terms to get,
[tex]\Rightarrow -\theta=-2\pi +\frac{5\pi}{3}[/tex]
We collect LCM to get,
[tex]\Rightarrow -\theta=\frac{-6\pi+5\pi}{3}[/tex]
We simplify to get,
[tex]\Rightarrow -\theta=-\frac{\pi}{3}[/tex]
We divide through by [tex]-1[/tex]
[tex] \theta=\frac{\pi}{3}[/tex] to get,
The correct answer is D.
