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Mrac [35]
3 years ago
8

Find the reference angle given: t= -5π/3.

Mathematics
1 answer:
Elina [12.6K]3 years ago
4 0

Answer:

The reference angle is \frac{\pi}{3}

Step-by-step explanation:

The given angle is t=-\frac{5\pi}{3}

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. <em>See diagram in attachment.</em>

Let \theta be the reference angle of  t=-\frac{5\pi}{3}


Then, from the diagram, we need to subtract \theta from -\frac{5\pi}{3} to get to -2\pi.


We can therefore write the following equation and solve for \theta.


\Rightarrow -\frac{5\pi}{3}-\theta=-2\pi


We group like terms to get,

\Rightarrow -\theta=-2\pi +\frac{5\pi}{3}

We collect LCM to get,

\Rightarrow -\theta=\frac{-6\pi+5\pi}{3}

We simplify to get,

\Rightarrow -\theta=-\frac{\pi}{3}

We divide through by -1

\theta=\frac{\pi}{3} to get,

The correct answer is D.







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