7.03 Graphs of trigonometric functions
Consider the function y = \sin x.
Complete the table of values giving answers in exact form:
| x | 0\degree | 30\degree | 90\degree | 150\degree | 180\degree | 210\degree | 270\degree | 330\degree | 360\degree |
|---|---|---|---|---|---|---|---|---|---|
| \sin x |
Sketch the graph of y = \sin x for 0 \leq x \leq 360.
State the sign of \sin 324 \degree.
Which quadrant would the angle 324 \degree lie?
Describe the trend of the graph of y = \sin x.
State the period of y = \sin x.
Given the unit circle below, state whether the following statements are true of the graph of y = \sin \theta:
The range of values of y = \sin \theta is -\infty \lt y \lt \infty.
The values of y = \sin \theta lie in the range - 1 \leq y \leq 1.
The graph of y = \sin \theta repeats after every 180 \degree.
The graph of y = \sin \theta repeats after every 360 \degree.
Consider the function y = \sin x.
State the y-intercept.
State the maximum y-value.
State the minimum y-value.
State the range of the function.
Determine whether the following statements are true of the curve y = \sin x.
The graph of y = \sin x is cyclic.
As x approaches infinity, the height of the graph approaches infinity.
The graph of y = \sin x is increasing between x = - 360 \degree and x = - 270 \degree.
The graph of y = \sin x is symmetric about the line x = 0.
The graph of y = \sin x is symmetric with respect to the origin.
The y-values of the graph repeat after a period of 180 \degree.
As x approaches infinity, the graph of y = \sin x stays between y = - 1 and y = 1.
Consider the function y = \sin x.
If one cycle of the graph of y = \sin x starts at x = 0 \degree, where does the next cycle start?
Describe whether the graph is increasing or decreasing in the following intervals:
- 270 \degree \lt x \lt - 90 \degree
- 450 \degree \lt x \lt - 270 \degree
90 \degree \lt x \lt 270 \degree
- 90 \degree \lt x \lt 90 \degree
Find the x-intercept in the following intervals:
0 \degree \lt x \lt 360 \degree
- 360 \degree \lt x \lt 0 \degree
Consider the function y = \cos x.
Complete the table of values giving answers in exact form:
| x | 0\degree | 60\degree | 90\degree | 120\degree | 180\degree | 240\degree | 270\degree | 300\degree | 360\degree |
|---|---|---|---|---|---|---|---|---|---|
| \cos x |
Sketch the graph of y = \cos x for 0 \leq x \leq 360.
State the sign of \cos 340 \degree.
State the quadrant where an angle with measure 340 \degree lie.
Given the unit circle below, state whether the following statements are true of the graph of \\ y = \cos \theta:
The values of y = \cos \theta lie in the range \\ - 1 \leq y \leq 1.
The range of values of y = \cos \theta is \\ -\infty \lt y \lt \infty.
The graph of y = \cos \theta repeats after every 180 \degree.
The graph of y = \cos \theta repeats after every 360 \degree.
Consider the function y = \cos x.
State the y-intercept.
State the maximum y-value.
State the minimum y-value.
State the domain of the function.
State whether the following statements are true of the graph of y = \cos x:
The graph of y = \cos x is cyclic.
As x approaches infinity, the height of the graph approaches infinity.
The graph of y = \cos x is increasing between x = 90 \degree and x = 180 \degree.
The graph of y = \cos x is symmetric about the line x = 0.
The graph of y = \cos x is symmetric with respect to the origin.
The y-values of the graph repeat after a period of 180 \degree.
As x approaches infinity, the graph of y = \cos x stays between y = - 1 and y = 1.
Consider the function y = \cos x.
If one cycle of the graph of y = \cos x starts at x = - 90 \degree, where does the next cycle start?
Describe whether the graph of y = \cos x is increasing or decreasing in the following intervals:
- 180 \degree \lt x \lt 0 \degree
- 360 \degree \lt x \lt - 180 \degree
0 \degree \lt x \lt 180 \degree
180 \degree \lt x \lt 360 \degree
Find the x-value of the x-intercepts in the following intervals:
0 \degree \lt x \lt 360 \degree
- 360 \degree \lt x \lt 0 \degree
Consider the equation y = \tan x.
Complete the table of values, giving answers in exact form. Write '-' if the value is undefined:
| x | 0\degree | 60\degree | 90\degree | 120\degree | 135\degree | 180\degree | 225\degree | 270\degree | 300\degree | 360\degree |
|---|---|---|---|---|---|---|---|---|---|---|
| \tan x |
Sketch the graph of y = \tan x for 0 \leq x \leq 360.
State the y-intercept.
State the sign of \tan 345 \degree.
State the quadrant where an angle with measure 345 \degree lie.
Given the unit circle below, state whether the following statements are true of the graph of y = \tan x:
The graph of y = \tan x repeats in regular intervals since the values of \sin x and \cos x repeat in regular intervals.
The graph of y = \tan x is defined for all values of x.
Since the radius of the circle is one unit, the value of the function y = \tan x lies in the region - 1 \leq y \leq 1.
The range of values of function \\ y = \tan x is -\infty \lt y \lt \infty.
By considering the graphs of the relevant trigonometric functions, evaluate the following:
\sin 90 \degree
\cos 90 \degree
\tan 90 \degree
\sin 180 \degree
\cos 180 \degree
\tan 180 \degree
\sin 270 \degree
\cos 270 \degree
\tan 270 \degree
\sin 360 \degree
\cos 360 \degree
\tan 360 \degree
Consider the function y = \sin \theta.
Find \theta if:
\sin \theta = \sin 390 \degree where \theta is in the 1st quadrant.
\sin \theta = \sin 480 \degree where \theta is in the 2nd quadrant.
\sin \theta = \sin 570 \degree where \theta is in the 3rd quadrant.
Consider the equation \sin x = \cos x in the domain 0 \degree \leq x \leq 360 \degree.
Sketch the graph of y = \sin x and y = \cos x on the same coordinate axes.
State the number of solutions of the equation \sin x = \cos x in the domain 0 \degree \leq x \leq 360 \degree.
Consider the curve y = \cos x for 0 \degree \leq x \leq 360 \degree.
How long is one cycle of the graph?
State the x-values for which:
Consider the curve y = \sin x for 0 \degree \leq x \leq 360 \degree.
How long is one cycle of the graph?
State the x-values for which:
Consider the curve y = \tan x for 0 \degree \leq x \leq 360 \degree.
How long is one cycle of the graph?
State the x-values for which:
Consider the function y = \cos x for - 180 \degree \leq x \leq 180 \degree.
Sketch the function.
State the x-values for which:
Consider the function y = \sin x for - 180 \degree \leq x \leq 180 \degree.
Sketch the function.
State the x-values for which:
Consider the function y = \tan x for - 180 \degree \leq x \leq 180 \degree.
Sketch the function.
State the x-values for which: