Chapter 9

In \(3-38,\) find each function value to four decimal places. $$ \cot 63^{\circ} $$

Use the definitions of \(\sin \theta\) and \(\cos \theta\) based on the unit circle to prove that \(\sin ^{2} \theta+\cos ^{2} \theta=1\)

The blades of a windmill make one complete rotation per second. How many rotations do they make in one minute?

In \(3-44,\) find the exact value. $$ \sin 450^{\circ} $$

In \(28-43,\) for each function value, if \(0^{\circ} \leq \theta <3 60^{\circ},\) find, to the nearest degree, two values of \(\theta\) \(\sin \theta=0.8090\)

In \(3-38,\) find each function value to four decimal places. $$ \sec 100^{\circ} $$

An airplane propeller rotates 750 times per minute. How many times will a point on the edge of the propeller rotate in 1 second?

In \(3-44,\) find the exact value. $$ \sin 0^{\circ}+\cos 0^{\circ}+\tan 0^{\circ} $$

In \(28-43,\) for each function value, if \(0^{\circ} \leq \theta <3 60^{\circ},\) find, to the nearest degree, two values of \(\theta\) \(\sin \theta=-0.0523\)

In \(3-38,\) find each function value to four decimal places. $$ \csc 125^{\circ} $$

The Ferris wheel at the county fair takes 2 minutes to complete one full rotation. a. To the nearest second, how long does it take the wheel to rotate through an angle of \(260^{\circ} ?\) b. How many minutes will it take for the wheel to rotate through an angle of \(1,125^{\circ} ?\)

In \(3-44,\) find the exact value. $$ \sin 45^{\circ}+\cos 60^{\circ} $$

In \(28-43,\) for each function value, if \(0^{\circ} \leq \theta <3 60^{\circ},\) find, to the nearest degree, two values of \(\theta\) \(\cos \theta=-0.3090\)

In \(3-38,\) find each function value to four decimal places. $$ \cot 165^{\circ} $$

The measure of angle \(P O A\) changes as \(P\) is rotated around the origin. The ratio of the change in the measure of the angle to the time it takes for the measure to change is called the angular speed of point \(P .\) For example, if a ceiling fan rotates 30 times per minute, its angular speed in degrees per minute is: \(30\left(360^{\circ}\right)=10,800^{\circ}\) per minute a. 3 times per minute b. 90 times per minute c. 600 times per minute

In \(3-44,\) find the exact value. $$ \sin 90^{\circ}+\cos 0^{\circ}+\tan 45^{\circ} $$

In \(28-43,\) for each function value, if \(0^{\circ} \leq \theta <3 60^{\circ},\) find, to the nearest degree, two values of \(\theta\) \(\cos \theta=0.9205\)

In \(3-38,\) find each function value to four decimal places. $$ \csc 245^{\circ} $$

In \(3-44,\) find the exact value. $$ \left(\cos 60^{\circ}\right)^{2}+\left(\sin 60^{\circ}\right)^{2} $$

In \(28-43,\) for each function value, if \(0^{\circ} \leq \theta <3 60^{\circ},\) find, to the nearest degree, two values of \(\theta\) \(\tan \theta=-9.5141\)

In \(3-38,\) find each function value to four decimal places. $$ \cot 254^{\circ} $$

In \(3-44,\) find the exact value. $$ \left(\sec 45^{\circ}\right)^{2}-\left(\tan 45^{\circ}\right)^{2} $$

In \(28-43,\) for each function value, if \(0^{\circ} \leq \theta <3 60^{\circ},\) find, to the nearest degree, two values of \(\theta\) \(\sin \theta=0.2419\)

In \(3-38,\) find each function value to four decimal places. $$ \sec 307^{\circ} $$

In \(3-44,\) find the exact value. $$ \left(\sin 30^{\circ}\right)\left(\cos 60^{\circ}\right) $$

In \(3-38,\) find each function value to four decimal places. $$ \csc 347^{\circ} $$

In \(3-44,\) find the exact value. $$ \left(\tan 45^{\circ}\right)\left(\cot 45^{\circ}\right) $$

In \(28-43,\) for each function value, if \(0^{\circ} \leq \theta <3 60^{\circ},\) find, to the nearest degree, two values of \(\theta\) \(\sin \theta=-0.1392\)

In \(39-50,\) find the smallest positive value of \(\theta\) to the nearest degree. $$ \sin \theta=0.3455 $$

In \(3-44,\) find the exact value. $$ \left(\sin 45^{\circ}\right)\left(\cos 45^{\circ}\right)\left(\tan 45^{\circ}\right) $$

In \(39-50,\) find the smallest positive value of \(\theta\) to the nearest degree. $$ \cos \theta=0.4383 $$

In \(3-44,\) find the exact value. $$ \left(\sin 30^{\circ}\right)\left(\sec 60^{\circ}\right) $$

In \(28-43,\) for each function value, if \(0^{\circ} \leq \theta <3 60^{\circ},\) find, to the nearest degree, two values of \(\theta\) \(\sin \theta=0\)

In \(39-50,\) find the smallest positive value of \(\theta\) to the nearest degree. $$ \tan \theta=0.2126 $$

In \(3-44,\) find the exact value. $$ \frac{\tan 30^{\circ}}{\cos 60^{\circ}} $$

In \(28-43,\) for each function value, if \(0^{\circ} \leq \theta <3 60^{\circ},\) find, to the nearest degree, two values of \(\theta\) \(\cos \theta=0\)

In \(39-50,\) find the smallest positive value of \(\theta\) to the nearest degree. $$ \cos \theta=0.7660 $$

In \(3-44,\) find the exact value. $$ \frac{\sin 45^{\circ}}{\cos 45^{\circ}} $$

In \(28-43,\) for each function value, if \(0^{\circ} \leq \theta <3 60^{\circ},\) find, to the nearest degree, two values of \(\theta\) \(\tan \theta=0\)

In \(39-50,\) find the smallest positive value of \(\theta\) to the nearest degree. $$ \tan \theta=0.7000 $$

In \(3-44,\) find the exact value. $$ \frac{\sin 30^{\circ}}{\csc 30^{\circ}} $$

In \(39-50,\) find the smallest positive value of \(\theta\) to the nearest degree. $$ \sin \theta=0.9990 $$

In \(39-50,\) find the smallest positive value of \(\theta\) to the nearest degree. $$ \cos \theta=0.9990 $$

Use a counterexample to show that \(\sin A+\sin B=\sin (A+B)\) is false.

In \(39-50,\) find the smallest positive value of \(\theta\) to the nearest degree. $$ \tan \theta=1.8808 $$

Use a counterexample to show that \(A < B\) implies cos \(A < \cos B\) is false.

In \(39-50,\) find the smallest positive value of \(\theta\) to the nearest degree. $$ \sin \theta=0.5446 $$

In \(39-50,\) find the smallest positive value of \(\theta\) to the nearest degree. $$ \cos \theta=0.5446 $$

In \(39-50,\) find the smallest positive value of \(\theta\) to the nearest degree. $$ \tan \theta=1.0355 $$

In \(39-50,\) find the smallest positive value of \(\theta\) to the nearest degree. $$ \tan \theta=12.0000 $$