Trigonometric Function

Subject: Optional Mathematics

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Overview

Different standard angles are taken as a variable in the trigonometric function. For different angles, the values of trigonometric ratios will also be different. Take the angles of x-axis and values of trigonometric ratios in y-axis Join the points freely to obtain the graph of the trigonometrical ratio.

Trigonometric Function

Graph of Trigonometric Function

Different standard angles are taken as a variable in the trigonometric function. For different angles, the values of trigonometric ratios will also be different. Take the angles of x-axis and values of trigonometric ratios in the y-axis. Join the points freely to obtain the graph of the trigonometrical ratio. For example: To draw the graph of y = sin x, we take x as standard angles 0o , 30o, 60o, 90o, 120o, 150o, 180o, 210o, 240o, 270o, 300o, 330o, 360o.

Some standard values of x and the corresponding values of sin x are given below:

x y = sinx
0
30° 0.5
45° 0.71
60° 0.87
90° 1
120° 0.87
135° 0.71
150° 0.5
180° 0
210° -0.5
225° -0.71
240° -0.87
270° -1
300° -0.87
315° -0.71
330° -0.5
360°  0

Plotting these values in the graph paper, we get the following graph. We get,

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Things to remember
x y = sinx
0
30° 0.5
45° 0.71
60° 0.87
90° 1
120° 0.87
135° 0.71
150° 0.5
180° 0
210° -0.5
225° -0.71
240° -0.87
270° -1
300° -0.87
315° -0.71
330° -0.5
360°  0
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Videos for Trigonometric Function
Example: Amplitude and period | Graphs of trig functions | Trigonometry | Khan Academy
Graphing trig functions
More trig graphs
Questions and Answers

soln: From the equation different values of y = sin3x:

x y=sin3x
0
10°\(\frac{π}{18}\) \(\frac{1}{2}\)(=0.5)
20°=\(\frac{π}{9}\) \(\frac{\sqrt{3}}{2}\)(=0.87)
30°=\(\frac{π}{6}\) 1
40°=\(\frac{2π}{9}\) \(\frac{\sqrt{3}}{2}\)(=0.87)
50°=\(\frac{\sqrt{5π}}{18}\) \(\frac{1}{2}\)(=0.5)
60°=\(\frac{π}{3}\) 0
70°=\(\frac{7π}{18}\) -\(\frac{1}{2}\)(=-0.5)
80°=\(\frac{4π}{9}\) -\(\frac{\sqrt{3}}{2}\)=-0.87
100°=\(\frac{5π}{9}\) -1
110°=\(\frac{11π}{18}\) -\(\frac{1}{2}\)=-0.50
120°=\(\frac{2π}{3}\) 0

150°\(\frac{5π}{6}\)

1
180°=π 0

graph of above table:

soln; Different values of y = sin2θ

θ y=sin2θ

30°\(\frac{π}{6}\)

60°

90°=\(\frac{π}{2}\)

120°=\(\frac{2π}{3}\)

150°=\(\frac{5π}{6}\)

180°=π

0

\(\begin{pmatrix} 1 \\ 2 \\ \end{pmatrix}\)2=\(\frac{1}{4}\)(=0.25)

\(\frac{\sqrt{3}}{2}\)2(=0.75)

1

\(\frac{\sqrt{3}}{2}\)2=0.75

\(\begin{pmatrix} 1 \\ 2 \\ \end{pmatrix}\)2=\(\frac{1}{4}\)=0.25

0=0

The graph o f the above table:

soln: Different values of y = cos2x

θ y=cos2x

0

30°=\(\frac{π}{6}\)

60°=\(\frac{π}{3}\)

90°=\(\frac{π}{2}\)

120°=\(\frac{2π}{3}\)

150°=\(\frac{5π}{6}\)

180°=π

0

\(\frac{1}{2}\)=0.5

\(\frac{-1}{2}\)=-0.5

-1

\(\begin{pmatrix} -1 \\ 2 \\ \end{pmatrix}\)=-0.5

\(\frac{1}{2}\)=0.5

1

The graph of above table:

Soln: Different values of y = cosθ - sinθ

θ

y=cosθ-sinθ

30°=\(\frac{π}{6}\)

60°=\(\frac{π}{3}\)

90°=\(\frac{π}{2}\)

120°=\(\frac{2π}{3}\)

150°=\(\frac{5π}{6}\)

180°=\(\frac{π}{2}\)

1

\(\frac{\sqrt{3}}{2}\)-\(\frac{1}{2}\)=0.87-0.5=0.37

\(\frac{1}{2}\)-\(\frac{\sqrt{3}}{2}\)=0.5-0.87=-0.37

0-1=-1

-\(\frac{1}{2}\)-\(\frac{\sqrt{3}}{2}\) = -0.5-0.87=-1.37

-\(\frac{\sqrt{3}}{2}\)-\(\frac{1}{2}\)=-0.87-0.5=-1.37

-1-0=1

The graph of above table:

soln: Different values of y = 2sinθ

θ y=2sinθ

30°=\(\frac{π}{6}\)

60°=\(\frac{π}{3}\)

90°=\(\frac{π}{2}\)

120°=\(\frac{2π}{3}\)

150°=\(\frac{5π}{6}\)

180°=\(\frac{π}{2}\)

0

1

\(\sqrt{3}\)=1.73

2

\(\sqrt{3}\)=1.73

1

0

The graph of the above table:

soln: Different values of y = tan2θ

θ

y=tan2θ

30°=\(\frac{π}{6}\)

60°=\(\frac{π}{3}\)

90°=\(\frac{π}{2}\)

120°=\(\frac{2π}{3}\)

150°=\(\frac{5π}{6}\)

180°=π

0

\(\sqrt{3}\)=1.73

-\(\sqrt{3}\)=-1.73

0

\(\sqrt{3}\)=1.73

-\(\sqrt{3}\)=-1.73

0

The graph of above table:

.

soln: Different values of y = tan\(\frac{3x}{2}\)

θ y=tan\(\frac{3x}{2}\)

30°=\(\frac{π}{6}\)

60°=\(\frac{π}{3}\)

90°=\(\frac{π}{2}\)

120°=\(\frac{2π}{3}\)

150°=\(\frac{5π}{6}\)

180°=π

0

1

-1

0

1

the grape of above table :

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