Consider the equation y = \tan x.
Complete the table with values in exact form:
| x | 0 | \dfrac{\pi}{4} | \dfrac{\pi}{2} | \dfrac{3 \pi}{4} | \pi | \dfrac{5 \pi}{4} | \dfrac{3 \pi}{2} | \dfrac{7 \pi}{4} | 2 \pi |
|---|---|---|---|---|---|---|---|---|---|
| \tan x |
Sketch the graph of y = \tan x on the domain -2\pi \leq 0 \leq 2\pi.
Graph the line y = 1 on the same coordinate plane.
Hence, state the exact solutions to the equation \tan x = 1 over this domain.
State the value of \tan \left(-2 \pi\right).
State the sign of \tan \left( \dfrac{- \pi}{6} \right).
State the sign of \tan \dfrac{9 \pi}{5}.
Which quadrant of a unit circle does an angle with measure \dfrac{9 \pi}{5} lie in?
Consider the graph of y = \tan x shown:
State the sign of \tan \dfrac{9 \pi}{5}.
Which quadrant does the angle \dfrac{9 \pi}{5} lie in?
Consider the unit circle shown:
Express \tan \theta in terms of \sin \theta and \cos \theta.
Does the graph of y = \tan x repeat in regular intervals? Explain your answer.
Consider the graph of y = \tan x for - 2 \pi \leq x \leq 2 \pi.
State the y-intercept of the graph.
State the period of the function.
State the equations of the vertical asymptotes on the domain 0 \leq x \leq 2\pi.
Does the graph of y=\tan x increase or decrease between any two successive vertical asymptotes?
If x \gt 0, find the least value of x for which \tan x = 0.
Consider the graph of y = \tan x for - 2 \pi \leq x \leq 2 \pi.
Select the word that best describes the graph:
Periodic
Decreasing
Even
Linear
Determine the range of y = \tan x.
As x increases, determine the equation of the next asymptote of the graph after x = \dfrac{7 \pi}{2}.
Consider the graph of y = \tan x for - 2 \pi \leq x \leq 2 \pi.
Determine the sign of \tan x for \\ \pi \leq x < \dfrac{3 \pi}{2}.
Determine the sign of \tan x for \\- \dfrac{\pi}{2} < x \leq 0.
Describe the function y = \tan x as odd, even or neither.
Consider the function y = \tan \theta.
\tan \theta is defined as \dfrac{\text{opposite }}{\text{adjacent }} for 0 \leq \theta < \dfrac{\pi}{2} in a right-angled triangle.
What happens to the value of \tan \theta as \theta increases from 0 to \dfrac{\pi}{2}?
The graph of y = \cos x for 0 \leq x \leq 2 \pi is provided. For what values of x is \cos x = 0?
Hence, for what values of x between 0 and 2 \pi is \tan x undefined?
Complete the table below:
| x | 0 | \dfrac{\pi}{4} | \dfrac{3 \pi}{4} | \pi | \dfrac{5 \pi}{4} | \dfrac{7 \pi}{4} | 2 \pi |
|---|---|---|---|---|---|---|---|
| \tan x |
Sketch that graph of y = \tan x for 0 \leq x \leq 2 \pi.
Which of the following terms describes the graph?
Periodic
Decreasing
Even
Linear
Which of the following terms is not an appropriate description of the graph of y = \tan x?
Amplitude
Range
Period
Asymptotes
State the period of y = \tan x in radians.
State the range of y = \tan x.
As x increases, what would be the next asymptote of the graph after x = \dfrac{7 \pi}{2}?