Sketch the two cycles of the graph (starting from x = 0) of the given function. Indicate the amplitude, period, phase shift, domain and range and vertical asymptotes.

Question

Sketch the two cycles of the graph (starting from x = 0) of the given function. Indicate the amplitude, period, phase shift, domain and range and vertical asymptotes.

1.   y = 4 sinx

2.   y = 7 cos 2x

3.   y = -4 cos (x-π/2) + 2

4.   y = -sec x

5.   y = tan 2x

Answer 1

Brenda's observation that you can graph them on your own calculator or demos.com will give you the "answers" to copy for the assignment.

But to understand how to do this for a quiz or a test, I think the best way to start understanding how to graph trigonometric functions is to understand that they all have 5 parts. Once you have this framework, you can then understand how each part affects the graph.

Trig -- The specified trigonometric function (sin, cos, tan, csc, sec, cot)

Each trig function has its own generic shape with a domain and range,

This shape is then modified by

A -- Amplitude (Multiply or Divide outside the trig function)

B -- Period (Multiply or Divide inside the trig function)

C -- Phase shift (+ or - inside the trig function)

D -- Horizontal shift (+ or - outside the trig function)

So generically, a trig function looks like

y = A Trig [B (x + C)] - D

I hope this helps. John