Examples of problems with other Trigonometric Functions

SUNY - New Paltz - Precalculus - Pindling

1. Use a calculator to graph f & g in the same viewing rectangle.
Show 2 periods and make a conjecture about the functions.

f(x) = sin x
g(x) = cos ()

    Plot f and g: Viewing Domain: [-2 Range [-2, 2]
    Period: 2 Amplitude: 1
    Conjecture: f(x) = g(x) same graphs

2. Sketch by hand and use a graphing utility to verify: y = cos 2x

    Period: Amplitude: 1
    Viewing Domain: [-2, 2] Range: [-2, 2]
    Key points: max (1,0), y=0(0, ¼ ), min(-1, ½ ), y=0(0, ¾ ), max(1,1)

3. Sketch by hand and use graphing utility to verify: y = 3 cos (x + ) - 3

    Period: 2, Amplitude: 3
    Shifts: lower bound solve x + = 0, x = -
                Upper bound solve x + = 2, x =3
    Viewing Domain [-3 , 3] Range: [-7, 7]

y = 3 cos (x + ) - 3

4. Sketch graph , show at least 2 periods and asymptotes

        Period: two consecutive asymptotes:
        Viewing Domain [- , ] Range: [-5, 5]
        Select [DrawDot] from [FORMAT] Menu

5. Sketch

        Graph first
        Period: = 4, so one cycle 0 to 4
        Viewing Domain [- , ] Range: [-6, 6]
        Select [DrawDot] from [FORMAT] Menu

Plot both in same viewing window

6. Sketch

        Graph first
        Period: so one cycle 0 to
        Viewing Domain [- , ] Range: [-4, 4]
        Select [DrawDot] from [FORMAT] Menu

Plot: Both y1 and y2