5.3 The other trigonometric functions  (Page 7/13)

$\tan \frac{\pi }{6}$

$\sec \frac{\pi }{6}$

$\csc \frac{\pi }{6}$

$\cot \frac{\pi }{6}$

$\tan \frac{\pi }{4}$

$\sec \frac{\pi }{4}$

$\csc \frac{\pi }{4}$

$\cot \frac{\pi }{4}$

$\tan \frac{\pi }{3}$

$\sec \frac{\pi }{3}$

$\csc \frac{\pi }{3}$

$\cot \frac{\pi }{3}$

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

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

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

$\cot \frac{13\pi }{6}$

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

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

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

$\cot \frac{11\pi }{4}$

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

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

$\csc \frac{2\pi }{3}$

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

$\tan \mathrm{225°}$

$\sec \mathrm{300°}$

$\csc \mathrm{150°}$

$\cot \mathrm{240°}$

$\tan \mathrm{330°}$

$\sec \mathrm{120°}$

$\csc \mathrm{210°}$

$\cot \mathrm{315°}$

If $\text{sin}t=\frac{3}{4},$ and $t$ is in quadrant II, find $\cos t,\sec t,\csc t,\tan t,\cot t.$

If $\text{cos}t=-\frac{1}{3},$ and $t$ is in quadrant III, find $\sin t,\sec t,\csc t,\tan t,\cot t.$

If $\tan t=\frac{12}{5},$ and $0\le t<\frac{\pi }{2},$ find $\sin t,\cos t,\sec t,\csc t,$ and $\cot t.$

If $\sin t=\frac{\sqrt{3}}{2}$ and $\cos t=\frac{1}{2},$ find $\sec t,\csc t,\tan t,$ and $\cot t.$

If $\sin \mathrm{40°}\approx 0.643\cos \mathrm{40°}\approx 0.766\text{sec}\mathrm{40°},\text{csc}\mathrm{40°},\text{tan}\mathrm{40°},\text{and}\text{cot}\mathrm{40°}.$

If $\text{sin}t=\frac{\sqrt{2}}{2},$ what is the $\text{sin}(-t)?$

If $\text{cos}t=\frac{1}{2},$ what is the $\text{cos}(-t)?$

If $\text{sec}t=3.1,$ what is the $\text{sec}(-t)?$

If $\text{csc}t=0.34,$ what is the $\text{csc}(-t)?$

If $\text{tan}t=-1.4,$ what is the $\text{tan}(-t)?$

If $\text{cot}t=9.23,$ what is the $\text{cot}(-t)?$

$\csc \frac{5\pi }{9}$

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

$\sec \frac{\pi }{10}$

$\tan \frac{5\pi }{8}$

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

$\csc \frac{\pi }{4}$

$\text{tan}\mathrm{98°}$

$\cot \mathrm{33°}$

$\cot \mathrm{140°}$

$\sec \mathrm{310°}$

If $\tan \left(t\right)\approx 2.7,$ and $\sin \left(t\right)\approx 0.94,$ find $\cos \left(t\right).$

If $\tan \left(t\right)\approx 1.3,$ and $\cos \left(t\right)\approx 0.61,$ find $\sin \left(t\right).$

If $\csc \left(t\right)\approx 3.2,$ and $\cos \left(t\right)\approx 0.95,$ find $\tan \left(t\right).$

If $\cot \left(t\right)\approx 0.58,$ and $\cos \left(t\right)\approx 0.5,$ find $\csc \left(t\right).$

Determine whether the function $f(x)=2\sin x\cos x$ is even, odd, or neither.

Determine whether the function $f(x)=3{\sin }^{2}x\cos x+\sec x$ is even, odd, or neither.

Determine whether the function $f(x)=\sin x-2{\cos }^{2}x$ is even, odd, or neither.

Determine whether the function $f(x)={\csc }^{2}x+\sec x$ is even, odd, or neither.

$\csc t\tan t$

$\frac{\sec t}{\csc t}$

The amount of sunlight in a certain city can be modeled by the function $h=15\cos \left(\frac{1}{600}d\right),$ where $h$ represents the hours of sunlight, and $d$ is the day of the year. Use the equation to find how many hours of sunlight there are on February 10, the 42 ^nd day of the year. State the period of the function.

The amount of sunlight in a certain city can be modeled by the function $h=16\cos \left(\frac{1}{500}d\right),$ where $h$ represents the hours of sunlight, and $d$ is the day of the year. Use the equation to find how many hours of sunlight there are on September 24, the 267 ^th day of the year. State the period of the function.

The equation $P=20\sin \left(2\pi t\right)+100$ models the blood pressure, $P,$ where $t$ represents time in seconds. (a) Find the blood pressure after 15 seconds. (b) What are the maximum and minimum blood pressures?

The height of a piston, $h,$ in inches, can be modeled by the equation $y=2\cos x+6,$ where $x$ represents the crank angle. Find the height of the piston when the crank angle is $\mathrm{55°}.$

The height of a piston, $h,$ in inches, can be modeled by the equation $y=2\cos x+5,$ where $x$ represents the crank angle. Find the height of the piston when the crank angle is $\mathrm{55°}.$