Trigonometric Functions

Use a calculator to find the approximate value of each expression rounded to two decimal places: $\csc \frac{5\pi }{13}$

Use a calculator to find the approximate value of each expression rounded to two decimal places:  $\sin 1$

Use a calculator to find the approximate value of each expression rounded to two decimal places: $\tan 1$

Use a calculator to find the approximate value of each expression rounded to two decimal places: $\sin 1°$

Use a calculator to find the approximate value of each expression rounded to two decimal places: $\tan 1°$

A point on the terminal side of an angle $\theta$ in standard position is given. Find the exact value of each of the six trigonometric functions of $\theta$: $(-3,4)$

A point on the terminal side of an angle $\theta$ in standard position is given. Find the exact value of each of the six trigonometric functions of $\theta$ : $(5,-12)$

A point on the terminal side of an angle $\theta$ in standard position is given. Find the exact value of each of the six trigonometric functions of $\theta$: $(2,-3)$

A point on the terminal side of an angle $\theta$ in standard position is given. Find the exact value of each of the six trigonometric functions of $\theta$: $(-1,-2)$

A point on the terminal side of an angle $\theta$ in standard position is given. Find the exact value of each of the six trigonometric functions of $\theta$ : $(-2,-2)$

A point on the terminal side of an angle $\theta$ in standard position is given. Find the exact value of each of the six trigonometric functions of $\theta$ : $(-1,1)$

A point on the terminal side of an angle $\theta$ in standard position is given. Find the exact value of each of the six trigonometric functions of $\theta$ : $\left(\frac{1}{3},\frac{1}{4}\right)$

A point on the terminal side of an angle $\theta$ in standard position is given. Find the exact value of each of the six trigonometric functions of $\theta$ : $(0.3, 0.4)$

Find the exact value of:$\sin 45°+\sin 135°+\sin 225°+\sin 315°$

Find the exact value of:$\tan 60°+\tan 150°$

Find the exact value of: $\sin 40°+\sin 130°+\sin 220°+\sin 310°$

Find the exact value of:$Tan 40°+Tan 140°$

If $f\left(\theta \right)=\sin \theta =0.1$,find $f(\theta +\pi )$

If $f\left(x\right)=\cos \theta =0.3,$find  $f(\theta +\pi )$

If $f\left(\theta \right)=\tan \theta =3$ find  $f \left(\theta +\pi \right)$.

If $f\left(\theta \right)=cot \theta =-2$ find $f\left(\theta +\pi \right)$.

If $\sin \theta =\frac{1}{5}$,find $csc \theta$.

If $\cos \theta =\frac{2}{3}$,find $sec \theta$.

If $f\left(\theta \right)=\sin \theta$ and $g\left(\theta \right)=\cos \theta$. Find the exact value of the function given below if $\theta =60°$.

Function $f\left(\theta \right)$

If $f\left(\theta \right)=\sin \theta$ and $g\left(\theta \right)=\cos \theta$. Find the exact value of the function given below if $\theta =60°$. Do not use a calculator.

Function is  $g\left(\theta \right)$.

If $f\left(\theta \right)=\sin \theta$ and $g\left(\theta \right)=\cos \theta$. Find the value of the function given below.  Do not use calculator.

Function is $f\left(\frac{\theta }{2}\right)$.

If $f\left(\theta \right)=\sin \theta$and $g\left(\theta \right)=\cos \theta$. Find the exact value of the  function given below if $\theta =60°$.Do not use calculator.

Function is $g\left(\frac{\theta }{2}\right)$.

If $f\left(\theta \right)=\sin \theta$ and $g\left(\theta \right)=\cos \theta$. Find the exact value of the function given below if $\theta =60°$. Do not use a calculator.

Function is ${\left[f\left(\theta \right)\right]}^2$.

If $f\left(\theta \right)=\sin \theta$ and $g\left(\theta \right)=\cos \theta$. Find the exact value of the function given below if $\theta =60°$. Do not use a calculator.

Function is ${\left[g\left(\theta \right)\right]}^2$.

If $f\left(\theta \right)=\sin \theta$ and $g\left(\theta \right)=\cos \theta$. Find the exact value of the  function given  below if $\theta =60°$. Do not use a calculator.

Function is $f\left(2\theta \right)$.

If $f\left(\theta \right)=\sin \theta$ and$g\left(\theta \right)=\cos \theta$ . Find the exact value of the function given  below if $\theta =60°$. Do not use a calculator.

Function is $g\left(2\theta \right)$.

If $f\left(\theta \right)=\sin \theta$ and $g\left(\theta \right)=\cos \theta$. Find the exact value of the function given below if $\theta =60°$.Do not use calculator.

Function is $2f\left(\theta \right)$.

If $f\left(\theta \right)=\sin \theta$ and $g\left(\theta \right)=\cos \theta$. Find the exact value of the  function given  below if $\theta =60°$. Do not use a calculator.

Function is $2g\left(\theta \right)$.

If $f\left(\theta \right)=\sin \theta$ and $g\left(\theta \right)=\cos \theta$. Find the exact value of the  function given below if $\theta =60°$. Do not use a calculator.

Function is $f\left(-\theta \right)$.

If $f\left(\theta \right)=\sin \theta$ and $g\left(\theta \right)=\cos \theta$. Find the exact value of the function given below  if $\theta =60°$. Do not use a calculator.

Function is $g\left(-\theta \right)$.

If $f\left(x\right)=\sin x ,g\left(x\right)=\cos x$ and $h\left(x\right)=2x , P\left(x\right)=\frac{x}{2}$.Find the value of the function $\left(f+g\right)\left(30°\right)$.

If $f\left(x\right)=\sin x ,g\left(x\right)=\cos x$ and $h\left(x\right)=2x ,P\left(x\right)=\frac{x}{2}$.Find the value of function $\left(f-g\right) \left(60°\right)$.

If $f\left(x\right)=\sin x ,g\left(x\right)=\cos x$ and $h\left(x\right)=2x ,P\left(x\right)=\frac{x}{2}$.Find the value of $\left(f·g\right) \left(\frac{3\pi }{4}\right)$.

If $f\left(x\right)=\sin x, g\left(x\right)=\cos x$ and $h\left(x\right)=2x ,P\left(x\right)=\frac{x}{2}$.Find the value of $\left(f·g\right) \left(\frac{4\pi }{3}\right)$.

If $f\left(x\right)=\sin x ,g\left(x\right)=\cos x$ and $h\left(x\right)=2x ,P\left(x\right)=\frac{x}{2}$.Find the value of $\left(f·h\right) \left(\frac{\pi }{6}\right)$.

If $f\left(x\right)=\sin x ,g\left(x\right)=\cos x$ and $h\left(x\right)=2x ,P\left(x\right)=\frac{x}{2}$.Find the value of $\left(g·p\right) \left(60°\right)$.

If $f\left(x\right)=\sin x ,g\left(x\right)=\cos x$ and $h\left(x\right)=2x, P\left(x\right)=\frac{x}{2}$.Find the value of the function $\left(p·g\right) \left(315°\right)$.

If $f\left(x\right)=\sin x ,g\left(x\right)=\cos x$ and $h\left(x\right)=2x ,P\left(x\right)=\frac{x}{2}$.Find the value of $\left(h·f\right) \left(\frac{5\pi }{6}\right)$.

If $f\left(x\right)=\sin x ,g\left(x\right)=\cos x$and $h\left(x\right)=2x ,P\left(x\right)=\frac{x}{2}$then,

Find the value of each of the following:

(a) Find $f\left(\frac{\pi }{4}\right)$ .What point is on the graph of f ?

(b) Assuming f is one to one use the result of part (a) to find a point on the graph of $f^{-1}$.

(c) What  point is on the graph of $y=f\left(x+\frac{\pi }{4}\right)-3$ if $x=\frac{\pi }{4}$.

If $f\left(x\right)=\sin x ,g\left(x\right)= \cos x,$and $h\left(x\right)=2x ,P\left(x\right)=\frac{x}{2}$then find the values of points given below.

(a) Find $g\left(\frac{\pi }{6}\right)$.What point is on the graph of g.

(b) Assuming g  one to one use the result of part (a) to find a point on the graph of $g^{-1}$.

(c) What point is on the graph of $y=2g\left(x-\frac{\pi }{6}\right)$ if $x=\frac{\pi }{6}$

Find two negative and three positive angles, expressed in radians, for which the point on the unit circle that corresponds  to each angle is $\left(\frac{1}{2},\frac{\sqrt{3}}{2}\right)$ .

Find two negative and three positive angles, expressed in radians ,for which the point on the unit circle that corresponds to each angle is $\left(\frac{-\sqrt{2}}{2} ,\frac{\sqrt{2}}{2}\right)$ .

Use a calculator in radian mode to complete the following table. What can you conclude about the value of $f\left(\theta \right)=\frac{\sin \theta }{\theta }$where $\theta$ approaches to 0.?

Use a calculator in radian mode to complete the following table.

What can you conclude about the value of $g\left(\theta \right)=\frac{\cos \theta -1}{\theta }$ as $\theta$ approaches to 0.

The projectile is fired at an angle of 45° to the horizontal with an initial speed of $100$ per second. Find the range R and maximum height H.