Question

complete this table:

angle (degrees)°	$sin\theta$	$cos\theta$	$\tan\theta$	angle (radians)
$30°$
$45°$
$60°$
$90°$
$120°$
$135°$
$150°$
$180°$
$210°$
$225°$
$240°$
$270°$
$300°$
$315°$
$330°$
$360°$

Explanation:

Step1: Convert degrees to radians

Use $\text{radians} = \text{degrees} \times \frac{\pi}{180}$

Step2: Find $\sin\theta$ values

Use unit circle standard values

Step3: Find $\cos\theta$ values

Use unit circle standard values

Step4: Calculate $\tan\theta$

Use $\tan\theta = \frac{\sin\theta}{\cos\theta}$

Answer:

Angle (degrees)°	$\sin\theta$	$\cos\theta$	$\tan\theta$	Angle (radians)
$30^\circ$	$\frac{1}{2}$	$\frac{\sqrt{3}}{2}$	$\frac{\sqrt{3}}{3}$	$\frac{\pi}{6}$
$45^\circ$	$\frac{\sqrt{2}}{2}$	$\frac{\sqrt{2}}{2}$	$1$	$\frac{\pi}{4}$
$60^\circ$	$\frac{\sqrt{3}}{2}$	$\frac{1}{2}$	$\sqrt{3}$	$\frac{\pi}{3}$
$90^\circ$	$1$	$0$	Undefined	$\frac{\pi}{2}$
$120^\circ$	$\frac{\sqrt{3}}{2}$	$-\frac{1}{2}$	$-\sqrt{3}$	$\frac{2\pi}{3}$
$135^\circ$	$\frac{\sqrt{2}}{2}$	$-\frac{\sqrt{2}}{2}$	$-1$	$\frac{3\pi}{4}$
$150^\circ$	$\frac{1}{2}$	$-\frac{\sqrt{3}}{2}$	$-\frac{\sqrt{3}}{3}$	$\frac{5\pi}{6}$
$180^\circ$	$0$	$-1$	$0$	$\pi$
$210^\circ$	$-\frac{1}{2}$	$-\frac{\sqrt{3}}{2}$	$\frac{\sqrt{3}}{3}$	$\frac{7\pi}{6}$
$225^\circ$	$-\frac{\sqrt{2}}{2}$	$-\frac{\sqrt{2}}{2}$	$1$	$\frac{5\pi}{4}$
$240^\circ$	$-\frac{\sqrt{3}}{2}$	$-\frac{1}{2}$	$\sqrt{3}$	$\frac{4\pi}{3}$
$270^\circ$	$-1$	$0$	Undefined	$\frac{3\pi}{2}$
$300^\circ$	$-\frac{\sqrt{3}}{2}$	$\frac{1}{2}$	$-\sqrt{3}$	$\frac{5\pi}{3}$
$315^\circ$	$-\frac{\sqrt{2}}{2}$	$\frac{\sqrt{2}}{2}$	$-1$	$\frac{7\pi}{4}$
$330^\circ$	$-\frac{1}{2}$	$\frac{\sqrt{3}}{2}$	$-\frac{\sqrt{3}}{3}$	$\frac{11\pi}{6}$
$360^\circ$	$0$	$1$	$0$	$2\pi$