Consider the equation y = \sin x.
Complete the table with values in exact form:
| x | 0 | \dfrac{\pi}{6} | \dfrac{\pi}{2} | \dfrac{5 \pi}{6} | \pi | \dfrac{7 \pi}{6} | \dfrac{3 \pi}{2} | \dfrac{11 \pi}{6} | 2 \pi |
|---|---|---|---|---|---|---|---|---|---|
| \sin x |
Sketch a graph for y = \sin x on the domain -2\pi \leq 0 \leq 2\pi.
State the value of \sin \left(-2 \pi\right).
State the sign of \sin \left( \dfrac{- \pi}{12} \right).
State the sign of \sin \dfrac{13 \pi}{12}.
Which quadrant of a unit circle does an angle with measure \dfrac{13 \pi}{12} lie in?
Consider the graph of y = \sin x given below:
Using the graph, what is the sign of \sin \dfrac{13 \pi}{12}?
Which quadrant does the angle \dfrac{13 \pi}{12} lie in?
Consider the curve y = \sin x drawn below:
If one cycle of the graph of y = \sin x starts at x = 0, when does the next cycle start?
List the regions on the graph that y = \sin x is decreasing.
State the x-intercept in the region 0 < x < 2 \pi.
Consider the curve y = \sin x:
State the x-intercept on the domain - 2 \pi < x < 0.
If one cycle of the graph of y = \sin x starts at x = -2\pi, at what value of x does the next cycle start?
Determine whether the graph of \\ y = \sin x is increasing or decreasing on the following domains:
\dfrac{\pi}{2} < x < \dfrac{3 \pi}{2}
\dfrac{3 \pi}{2} < x < \dfrac{5 \pi}{2}
- \dfrac{3 \pi}{2} < x < - \dfrac{\pi}{2}
- \dfrac{5 \pi}{2} < x < - \dfrac{3 \pi}{2}
Consider the graph of y = \sin x and determine whether the following statements are true or false:
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 2 \pi.
Consider the graph of y = \sin x.
Write an expression in terms of n to describe the x-intercepts of the function, where the angle x is measured in radians and n is an integer.
Consider the equation y = \cos x.
Complete the table with values in exact form:
| x | 0 | \dfrac{\pi}{3} | \dfrac{\pi}{2} | \dfrac{2 \pi}{3} | \pi | \dfrac{4 \pi}{3} | \dfrac{3 \pi}{2} | \dfrac{5 \pi}{3} | 2 \pi |
|---|---|---|---|---|---|---|---|---|---|
| \cos x |
Sketch a graph for y = \cos x on the domain -2\pi \leq 0 \leq 2\pi.
State the value of \cos \pi.
State the sign of \cos \left( \dfrac{- \pi}{4} \right).
State the sign of \cos \dfrac{11 \pi}{6}.
Which quadrant of a unit circle does an angle with measure \dfrac{11 \pi}{6} lie in?
Consider the following unit circle:
State the range of y = \cos x.
State the range of y = \sin x.
How often does the graph of y = \cos x repeat?
How often does the graph of y = \sin x repeat?
Consider the curve y = \cos x drawn below:
What are the x-intercepts in the region - 2 \pi < x < 0?
As x approaches infinity, what y-values does the graph of y = \cos x stay between?
List the regions on the graph that y = \cos x is increasing.
Consider the functions y = \sin x and y = \cos x.
State the amplitude of both the graphs of these functions.
State the period of both the graphs of these functions.
Consider the graph of y = \cos x and determine whether the following statements are true or false:
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 \pi.
Consider the graph of y = \cos x.
Write an expression in terms of n to describe the x-intercepts of the function, where the angle x is measured in radians and n is an integer.
Consider the following graphs f(x)=\sin x and g(x)=\cos x:
Describe the graph of g(x) in terms of a transformation of the graph of f(x).