Trigonometry - Complementary and Supplementary Angles

Determine the value for $sin (150^{\circ})$ in radical form.

$\frac{1}{2}$

Explanation

According to the unit circle, an angle of $150^{\circ}$ is similar to an angle of $30^{\circ}$ .

Unit_circle

Therefore:

$sin (150^{\circ}) = sin (30^{\circ}) = \frac{1}{2}$

What is the relationship between angles 1 and 2?

Screen_shot_2014-02-15_at_6.57.52_pm

supplementary

complimentary

vertical

horizontal

equal

Explanation

These angles are supplementary, as the sum of the angles is 180o.

What angle is supplementary to $34^\circ$ ?

$146^\circ$

$56^\circ$

$124^\circ$

$214^\circ$

$326^\circ$

Explanation

Two angles that are supplementary add up to $180^\circ$ . For our problem, that means that $x+34^\circ=180^\circ$ .

Subtract $34^\circ$ from both sides.

$x=180^\circ-34^\circ$

$x=146^\circ$

Find the complementary angle to $\frac{\pi}{4}$

$\frac{\pi}{4}$

$-\frac{\pi}{4}$

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

$\frac{7\pi}{4}$

$-\frac{5\pi}{4}$

Explanation

Two angles that are complementary must add to $\frac{\pi}{2}$ , therefore we subtract the given angle from $\frac{\pi}{2}$ as follows:

$\frac{\pi}{2} - \frac{\pi}{4} = \frac{2\pi}{4} - \frac{\pi}{4} = \frac{\pi}{4}$

Find the angle that is supplementary to $45^{\circ}$

$135^{\circ}$

$45^{\circ}$

$-45^{\circ}$

$315^{\circ}$

$-225^{\circ}$

Explanation

Two angles are supplementary if their sum is $180^{\circ}$ , therefore we subtract the given angle from $180^{\circ}$ as follows:

$180^{\circ} - 45^{\circ} = 135^{\circ}$

Find the complementary angle to $\frac{\pi}{12}$

$\frac{5\pi}{12}$

$-\frac{\pi}{12}$

$\frac{11\pi}{12}$

$-\frac{5\pi}{12}$

$\frac{23\pi}{12}$

Explanation

Two angles are complementary if their sum is $\frac{\pi}{2}$ , therefore we subtract the given angle from $\frac{\pi}{2}$ as follows:

$\frac{\pi}{2} - \frac{\pi}{12} = \frac{6\pi}{12} - \frac{\pi}{12} = \frac{5\pi}{12}$

Find the angle that is supplementary to $179^{\circ}$

$1^{\circ}$

$-179^{\circ}$

$180^{\circ}$

$-180^{\circ}$

$181^{\circ}$

Explanation

Two angles are supplementary if their sum is $180^{\circ}$ , therefore we subtract the given angle from $180^{\circ}$ as follows:

$180^{\circ} - 179^{\circ} = 1^{\circ}$

Find the angle that is supplementary to $\frac{7\pi}{8}$

$\frac{\pi}{8}$

$-\frac{\pi}{8}$

$-\frac{7\pi}{8}$

$\frac{9\pi}{8}$

$-\frac{3\pi}{8}$

Explanation

If two angles are supplementary their sum is $\pi$ , therefore we subtract the given angle from $\pi$ as follows:

$\pi - \frac{7\pi}{8} = \frac{8\pi}{8} - \frac{7\pi}{8} = \frac{\pi}{8}$

Find the complementary angle to $17^{\circ}$

$73^{\circ}$

$-17^{\circ}$

$163^{\circ}$

$-73^{\circ}$

$117^{\circ}$

Explanation

In order for two angles to be complementary their sum must be $90^{\circ}$ , therefore the complementary angle can be found by subtracting the given angle from $90^{\circ}$ :

$90^{\circ} - 17^{\circ} = 73^{\circ}$

Determine the complementary angle to $90^{\circ}$

$0^{\circ}$

$-90^{\circ}$

$90^{\circ}$

$10^{\circ}$

$270^{\circ}$

Explanation

The sum of two complementary angles must be $90^{\circ}$ , therefore in order to determine the complementary angle of $90^{\circ}$ we simply subtract from $90^{\circ}$ as follows:

$90^{\circ} - 90^{\circ} = 0^{\circ}$

Complementary and Supplementary Angles

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