Trigonometric Curves

The three main trigonometric graphs are:

  • Sine graph
  • Cosine graph
  • Tan graph

Sine Graph

sinegraph
x0 sin x
00
901
1800
270-1
3600

Characteristics:

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

Cosine Graph

cosgraph
x0 cos x
01
900
180-1
2700
3601

Characteristics:

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

Tan Graph

tangraph
x0 tan x
00
90
1800
270
3600

Characteristics:

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

Transformation of a Graph

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

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.

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

 

 

 

Recommended Reading

 

Maths is challenging; so is finding the right book. K A Stroud, in this book, cleverly managed to make all the major topics crystal clear with plenty of examples; popularity of the book speak for itself - 7th edition in print.

amazon icon Amazon Ad

Advertisement