Consider the trigonometric ratio \sin x.
Given the values of \sin x for angles in the first quadrant, complete the following table of values:
| x | 0 \degree | 30 \degree | 45 \degree | 60 \degree | 90 \degree | 120 \degree | 135 \degree | 150 \degree | 180 \degree |
|---|---|---|---|---|---|---|---|---|---|
| \sin x | 0 | 0.5 | 0.71 | 0.87 | 1 | 0 |
| x | 210 \degree | 225 \degree | 240 \degree | 270 \degree | 300 \degree | 315 \degree | 330 \degree | 360 \degree |
|---|---|---|---|---|---|---|---|---|
| \sin x | -1 | 0 |
Hence sketch the graph of y = \sin x for 0\degree \leq x \ \leq 360 \degree.
State the coordinates of the y-intercept.
State the range of the y-values.
Consider the function y = \sin x.
Complete the table, writing the values of \sin x 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 the graph for y = \sin x for -2\pi \leq x \leq 2\pi.
Hence state the sign of the following ratios:
In which quadrant of a unit circle do the following angles lie?
Use the diagram of the unit circle to explain the following properties of the graph of \\y=\sin x:
The range of values for y=\sin x is \\ -1 \leq y \leq 1.
The graph of y=\sin x repeats after every 2\pi radians.
Consider the graph of y = \sin x:
If one cycle of the graph of y = \sin x starts at x = 0, 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{\pi}{2}
\dfrac{\pi}{2} < x < \dfrac{3 \pi}{2}
- \dfrac{5 \pi}{2} < x < - \dfrac{3 \pi}{2}
- \dfrac{3 \pi}{2} < x < - \dfrac{\pi}{2}
State the x-intercept on the domain 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, writing the values of y = \cos x 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 the graph for y = \cos x for -2\pi \leq x \leq 2\pi.
Hence state the sign of the following ratios:
In which quadrant of a unit circle do the following angles lie?
Consider the graph of y=\cos x:
State the coordinates of the y-intercept.
State the range of the function.
State the period of the function.
Determine the x-intercepts on the domain 0 < x < 2 \pi.
Consider the graph of y = \cos x:
If one cycle of the graph of y = \cos x starts at x = - \dfrac{\pi}{2}, at what value of x does the next cycle start?
Determine whether the graph of \\ y = \cos x is increasing or decreasing on the following regions:
- 2 \pi < x < - \pi
- \pi < x < 0
0 < x < \pi
\pi < x < 2 \pi
Consider the graph of y = \cos x:
State the x-intercepts on the domain - 2 \pi < x < 0.
If one cycle of the graph of y = \cos x starts at x = -\dfrac{3\pi}{2}, at what value of x does the next cycle start?
Determine whether the graph of \\ y = \cos x is increasing or decreasing on the following domains:
0 < x < \pi
- \pi < x < 0
- 2 \pi < x < - \pi
\pi < x < 2 \pi
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).