I. The Graph of f(x) = sin x.

Graph the function f(x) = sin x with x as the independent variable and

f(x) = sin x as the dependent variable. “x” can represent an angle, or a real number.

  1. Complete the table below.
  1. Graph f(x) = sin x from your table on the grid below. Plot the points and connect them with a smooth curve.


  1. Set your calculator to Radians Mode. Enter y1 = sin x.

Set the window for x: Xmin = -2

Xmax = 2

Xscl = /2

Ymin = -2

Ymax = 2

Yscl = 1

Press Graph. Check your graph against the graph on the calculator.

Now change the window: Xmin = -4

Xmax = 4

  1. What does the graph look like for x > 2? ______

Starting at x = 0, the graph completes one complete cycle at

x = 2. Therefore, the sine function is periodic and has a period of P = 2.

Reset the window to: Xmin = -2

Xmax = 2

Answer the following questions for x in this interval [-2π, 2π].

  1. The maximum value of f(x) is ______.

Where does f(x) reach its maximum?______

  1. The minimum value of f(x) is ______.

Where does f(x) reach its minimum?______

7. Domain: ______

Range: ______

8. X-Intercepts: ______

Y-Intercept: ______

9. f(x) = sin x is an ______function. (Even or Odd)

II. The Graph of f(x) = cos x.

Graph the function f(x) = cos x with x as the independent variable and

f(x) = cos x as the dependent variable.

  1. Complete the table below.
  1. Graph f(x) = cos x from your table on the grid below.


  1. On your calculatorenter y1 = cos x. Graph using the same window.

Check your graph against the graph on the calculator.

  1. The graph of f(x) = cos x is periodic. The periodis how long it takes to complete one full cycle. The period is P = ____.
  1. The maximum value of f(x) is ______.

Where does f(x) reach its maximum?______

  1. The minimum value of f(x) is ______.

Where does f(x) reach its minimum?______

  1. Domain: ______

Range: ______

  1. X-Intercepts: ______

Y-Intercept: ______

  1. f(x) = cos x is an ______function. (Even or Odd)

10. The graphs of f(x) = sin x and f(x) = cos x are called sinusoidal functions.


III. The Graph of f(x) = tan x.

Graph the function f(x) = tan x with x as the independent variable and

f(x) = tan x as the dependent variable.

1. Complete the table below.

  1. Graph f(x) = tan x from your table on the grid below. Recall that an undefined value will produce a vertical asymptote. Draw the vertical asymptotes as dashed lines. Draw the curves toward the vertical asymptotes.

Note: is midway between and .


  1. On your calculator enter y1 = tan x.

Set the window to: Ymin = -4

Ymax = 4

Press Graph. Your graph should look like the graph on the calculator with the vertical asymptotes drawn.

3. The Period of f(x) = tan x is P = ____.

4. The vertical asymptotes are ______.

6. Domain: ______

Range: ______

7. X-Intercepts: ______

Y-Intercept: ______

8. f(x) = tan x is an ______function. (Even or Odd)