7.4 The other trigonometric functions  (Page 7/14)

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

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

If $\sin \mathrm{40°}\approx 0.643$ and $\cos \mathrm{40°}\approx 0.766,$ find $\text{sec}\mathrm{40°},\text{csc}\mathrm{40°},\text{tan}\mathrm{40°},$ 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 $\text{tan}t=\mathrm{-1.4},$ 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 267th 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 $\mathrm{55°}.$

$\frac{\pi }{4}$

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

$\mathrm{-210°}$

$\mathrm{180°}$

Find the length of an arc in a circle of radius 7 meters subtended by the central angle of $\mathrm{85°}.$