Graphs of Trigonometric Functions: Video e Problemi di Pratica

Find the amplitude and period for the given trigonometric expression below.

$P\left(x\right)=3\sin \left(4x\right)$

Find the amplitude and period for the given trigonometric expression below.

$P\left(x\right)=5\cos \left(\frac{x}{4}\right)$

Find the amplitude and period for the given trigonometric expression below.

$P\left(x\right)=5.7\sin \left(\frac{1}{9}(x-7)\right)$

Find the amplitude and period for the given trigonometric expression below.

$P\left(x\right)=6.4\cos \left(\frac{\pi x}{15}\right)$

Draw the graph of the following trigonometric function using transformation from the basic trigonometric function.

$f\left(x\right)=2\cos \left(\frac{\pi x}{18}\right)+3$

Create a sine function out of the given information below:

Period = $6$

Minimum value = $-6$ when $x=1$

Maximum value = $10$ when $x=4$

Describe the following graph using a cosine function.

Determine the period $T$ and sketch the graph of the given function:

$y=\cos \left(\frac{\pi x}{4}\right)$

Graph the function $y=\sin 2x$ and determine its period. Consider only one period when graphing.

Graph the function $y=-\cos 4\pi x$ and determine its period. Consider only one period when graphing.

Graph the function $y=\sin (x-\frac{\pi }{2})+2$ and determine its period. Consider only one period when graphing.

Graph the function $y=-\tan 2\pi x$. Determine its period and the type of symmetry it exhibits. Consider only one period when graphing.

Graph the functions $y=\sin x$ and $y=\csc x$ on the same coordinate plane and consider the domain $-\pi \le x\le \pi$. Describe the relationship between the two graphs.

Graph the functions $y=\cos x$ and $y=\lfloor \cos x\rfloor$ on the same coordinate plane. Consider only one period when graphing. Determine the domain and range of $y=\lfloor \cos x\rfloor$.

Sketch the graph of the function below. Note: The window should give a picture of the overall behavior of the function.

$y=4\sin (20x-\frac{\pi }{3})$

Sketch the graph of the function below. Note: The window should give a picture of the overall behavior of the function.

$y=5\cos (15x-\frac{\pi }{4})+2$

Sketch the graph ($2$ periods) of the function below. Note: The window should give a picture of the key features of the function.

$f\left(x\right)=3\cos (2x-\frac{\pi }{4})+1$

Draw the graph ($2$ periods) of the function below. Note: The window should give a picture of the key features of the function.

$f\left(x\right)=3\sin (2x-\frac{2\pi }{3})-1$

Draw the graph of the given function. Note: The window should give a picture of the key features of the function.

$f\left(x\right)={\sin }^3{(2x-\frac{\pi }{3})}^{}$

Consider the general formula $f\left(x\right)=A\sin \left(\frac{2\pi }{B}(x-C)\right)+D$ that defines a set of curves. Determine $A$, $B$, $C$, and $D$ and sketch the graph of the function below.

$y=-2\sin \left(\frac{2\pi }{5}(x-3)\right)+4$

Consider the general formula $f\left(x\right)=A\sin \left(\frac{2\pi }{B}(x-C)\right)+D$ that defines a set of curves. Find $A$, $B$, $C$, and $D$ and sketch the graph of the function below.

$y=-3\sin \left(\frac{2\pi }{7}(x-\frac{7}{6})\right)+4$

Graph the function below. Note: The window should give a picture of the key features of the function.

$f\left(x\right)=\sin \left(4x\right)+\cos \left(4x\right)$