Precalculus Trigonometry (4.1-4.3)

Use a calculator to evaluate the trigonometric function. Round your answer to four decimal places.

sec 1.8

Evaluate the trigonometric function using its period as an aid.

sin $\frac{19\pi}{4}$   

•  $\frac{\sqrt{2}}{2}$  

•  $\ -\ \frac{\sqrt{2}}{2}$  

•  $\frac{1}{2}$  

•  $\frac{\sqrt{2}}{3}$  

Convert the angle measure from degrees to radians. Round to three decimal places if you choose to write in that form.

 $532\degree$  

•   $9.284\ =\ \frac{12\pi}{5}$  

•  $9.280\ =\ \frac{133\pi}{45}$  

•  $9.325\ =\ \frac{15\pi}{6}$  

•  $9.477\ =\frac{17\pi}{2}$  

Convert the angle measure from radians to degrees. Round to three decimal places.

 $\frac{15\pi}{8}$  

•  $333.500$  

•  $337.500\degree$  

•  $323.513\degree$  

•  $\pi$  

Determine two coterminal angles (one positive and one negative) for each angle. Give your answer in radians.

 $-\frac{11\pi}{6}$  

•  $\frac{\pi}{7}\ and\ -\frac{13\pi}{6}$  

•  $\frac{3\pi}{2}\ and\ -\ \frac{17\pi}{2}$  

•  $\frac{\pi}{6}\ and\ \ -\frac{23\pi}{6}$  

•  $-\frac{\pi}{6}\ and\ \frac{13\pi}{6}$  

 $\frac{5\pi}{3}$  Find the point (x,y) on the unit circle that corresponds to the real number t.

•  $\left(-\frac{1}{2},\ \frac{\sqrt{3}}{2}\right)$  

•  $\left(\frac{\sqrt{2}}{2},\ \frac{\sqrt{2}}{2}\right)$  

•  $\left(\frac{1}{2},\ -\frac{\sqrt{3}}{2}\right)$  

•  $\left(\frac{1}{2},\ \frac{\sqrt{3}}{2}\right)$  

Evaluate (if possible) the sine and cotangent functions of the real number.
 $\frac{4\pi}{3}$  

•  $\sin\ t\ =\ \frac{\sqrt{3}}{2}\ and\ \cot\ t=\sqrt{3}$  

•  $\sin t\ =\ \frac{1}{2}\ and\ \cot\ t=\frac{\sqrt{3}}{2}$  

•  $\sin t\ =\ \frac{\sqrt{2}}{2}\ and\ \cot\ t=\frac{1}{2}$  

•  $\sin\ t\ =\ -\frac{\sqrt{3}}{2}\ and\ \cot\ t\ =\ \frac{\sqrt{3}}{3}$  

Use the given value(s), and the trigonometric identities, to find the indicated trigonometric functions.
Given:
 $\sec\ \theta=5\ and\ \tan\ \theta\ =2\sqrt{6}$  

FIND:  $\cos\ \theta,\ \cot\ \theta,\ and\ \sin\ \theta$  

•  $\cos\ \theta\ =\ \frac{1}{5},\ \cot\ \theta=\sqrt{3},\ and\ \sin\ \theta=\frac{\sqrt{3}}{2}$  

•  $\cos\ \theta=5,\ \cot\ \theta=\frac{1}{5},\ and\ \sin\ \theta=\ \frac{\sqrt{6}}{12}$  

•  $\cos\ \theta=\frac{1}{5},\ \cot\ \theta=\frac{\sqrt{6}}{12},\ and\ \sin\ \theta=\frac{2\sqrt{6}}{5}$  

•  $\cos\ \theta=\frac{1}{2},\ \cot\ \theta=\frac{\sqrt{5}}{3},\ and\ \sin\ \theta=\ 3$  

Use a calculator to evaluate the function. Round your answer to four decimal places.
 $\cot\ 66.5\degree$  

Find the values of the angle in degrees and radians without the aid of a calculator. (HINT: use Quadrant I)

 $\cot\ \theta=\frac{\sqrt{3}}{3}$  

•  $\theta=\ 45\degree\ or\ \frac{\pi}{4}$  

•  $\theta=30\degree\ or\ \frac{\pi}{6}$  

•  $\theta=90\degree\ or\ \frac{\pi}{2}$  

•  $\theta\ =60\degree\ or\ \frac{\pi}{3}$