Radians and the Unit Circle

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SAT Math › Radians and the Unit Circle

Questions 1 - 3

1

The degree angle can be expressed as what in radians?

$\frac{5}{3}\pi$

$\frac{6}{5}\pi$

$\frac{7}{6}\pi$

$\frac{11}{6}\pi$

$\frac{4}{3}\pi$

Explanation

In order to convert degrees to radians, we will need to know the conversion factor.

$180 \textup{ deg} = \pi \textup{ rad}$

Set up a dimensional analysis to solve.

$300 \textup{ deg} (\frac{\pi \textup{ rad}}{180 \textup{ deg}}) = \frac{5}{3}\pi\textup{ rad}$

The answer is: $\frac{5}{3}\pi$

2

Which of the following angles belong in the fourth quadrant?

$\frac{17}{9}\pi$

$\frac{4}{3}\pi$

$\frac{5}{2}\pi$

$\pi$

Explanation

The fourth quadrant is in the positive x-axis and negative y-axis.

The angle ranges are:

$270\rightleftharpoons 360 \textup{ deg}$

$\frac{3}{2}\pi\rightleftharpoons 2\pi \textup{ radians}$

The only possible answer is: $\frac{17}{9}\pi$

3

What degree measure is equivalent to $4\pi$ ?

Explanation

Every pi radians is equal to 180 degrees.

Replace the pi term with 180 degrees and multiply.

$4\pi = 4(180 \textup{ degrees}) = 720$

The answer is:

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