Practice Sine function
The sine function describes a repeating oscillation, with amplitude, period and shifts controlling its graph.
It is useful for modelling periodic signals.
Exercises with solutions
The sine function f(x) = sin x assigns to every angle a value between −1 and 1. It repeats periodically: after 360° it starts again. In the form f(x) = a · sin(b · x), a is the amplitude, half the height of the wave, and the period is 360° ÷ b.
Exercise 1
What is the largest value sin x can take?
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1 and −1
The sine always lies between −1 and 1. The largest value is 1, the smallest −1.
Exercise 2
How large is sin 90°?
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1
At 90° the sine curve reaches its highest point, the value 1.
Exercise 3
What is the amplitude of f(x) = 3 · sin x?
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3
The factor in front of the sine is the amplitude. The curve oscillates between −3 and 3.
Exercise 4
What is the period of f(x) = sin(2x)?
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180°
The period is 360° ÷ b = 360° ÷ 2 = 180°.
Common mistake
Confusing amplitude and period: the factor in front of the sine stretches the height (amplitude), the factor inside the argument compresses the width (period = 360° ÷ b). And confusing range with domain: sin x is defined for every angle but only produces values between −1 and 1.
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