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TRIGONOMETRIC GRAPHS
Higher Tier
GRAPHS OF TROGONOMETRIC RATIOS

The graphs of y = sin x, y = cos x and y = tan x are widely used in electrical engineering,
electronics, sound engineering and all studies of waves.

You need to sketch the graphs of these trigonometric functions.

You need to identify important facts about each of these graphs and remember their
symmetry.

You need to use these graphs to solve simple trigonometric equations.
Accurate Graphs (for 0°  x  360°)
triggraphs
©RSH 12 April 2010

Passes through
the origin, 180°,
360°

Maximum 1
when
x = 90° and
Minimum 1.

The AMPLITUDE
is 1

Repeats every
360°

Graph can be
continued both
ways indefinitely.

Maximum 1
when
x = 0° and
Minimum 1.

The AMPLITUDE
is 1

Repeats every
360°

Graph can be
continued both
ways indefinitely.
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TRIGONOMETRIC GRAPHS
Higher Tier

Passes through
the origin, 180°,
360°

Maximum 
when x = 90°

Minimum 

The vertical lines
at x = 90°, 180°
etc are called
ASYMPTOTES.

Repeats every
180°

Graph can be
continued both
ways indefinitely.
Solving Equations
Solve the equation sin x = 0.5
giving all values in the range
0°  x  360°
Solution
Using a calculator, x  sin1 0.5
To give x = 30°.
Looking at the graph of y = sin
x, sin x = 0.5 twice in this range.
x = 30° is the first, the second is
180°  30° = 150°.
Answer: x = 30° and 150°
Note: The answers can be checked in a calculator
triggraphs
©RSH 12 April 2010
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TRIGONOMETRIC GRAPHS
Higher Tier
Solve the equation cos x = 0.5
giving all values in the range
90°  x  360°
Solution
Using a calculator, x  cos1 0.5
To give x = 60°.
Looking at the graph of y = cos
x, cos x = 0.5 three times in this
range.
x = 60° is the first,
the second is 60° and
the third is 360°  60° = 300°.
Answer: x = 60°, 60°, 300°
Solve the equation tan x = 1
giving all values in the range
90°  x  360°
Solution
Using a calculator, x  tan1 0.5
To give x = 45°.
Looking at the graph of y = tan
x, tan x = 1 three times in this
range.
x = 45° is the first,
the second is 180°  45° = 135°
and
the third is 360°  45° = 315°.
Answer: x = 45°, 135°, 315°
Solve the equation sin x = 0.3
giving all values in the range
0°  x  360°
Solution
Using a calculator,
x  sin1(0.3)
To give x = 17.5°.
Answer: x = 197.5°, 342.5°
triggraphs
©RSH 12 April 2010
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