Data Handling

Trigonometric Graphs

The three main trigonometric graphs are:
  • Sine graph
  • Cosine graph
  • Tan graph

Sine Graph


x0 sin x
00
901
1800
270-1
3600

sinegraph
Characteristics:
  • Period is 3600. It repeats itself every 360 degrees.
  • Maximum value = +1
  • Minimum value = -1

Cosine Graph


x0 cos x
01
900
180-1
2700
3601

cosgraph
Characteristics:
  • Period is 3600. It repeats itself every 360 degrees.
  • Maximum value = +1
  • Minimum value = -1

Tan Graph


x0 tan x
00
90∞
1800
270∞
3600

tangraph
Characteristics:
  • Period is 1800. It repeats itself every 180 degrees.
  • Maximum value = +∞
  • Minimum value = -∞

Transformation of a Graph


x0sin x2 sin x1 + 2 sin x
0001
90123
180001
270-1-2-1
360001

transformation
This is stretched by a factor 2 parallel to the y-axis and then moved up by 1 - a translation of 1 in the positive y-axis.

Practice is the key to mastering maths; please visit this page, for more worksheets.


Now, in order to complement what you have just learnt, work out the following questions:


    1) Sketch the following graphs:
    • 2 cos x
    • 1 - 3 sin x
    • 2 tan x
    • 2 + 3 sin x

    2) Find the period, maximum value and minimum value of the following functions:
    • 3 cos x
    • 1 - 2sin 2x
    • 3 cos 2x
    • 2 + 3 sin x/2