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Questions > Grade 22 Precalculus > Trigonometric Functions -Graphs of Sine and Cosine: Sinusoids

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Question: State the amplitude and period of the given sinusoidal function y = - 3 sin (x - π6) + 1.

A ) + 3 , + π2
B ) - 3 , 2π
C ) + 3 , - 2π
D ) + 3 , + 2π

Steps to derive

1 y = - 3 sin(x - π6) + 1

2 The amplitude of the sinusoid f(x) = a sin(bx + c) + d is |a|.
[Formula.]

3 Hence, the amplitude of given sinusoid is |a| = 3 .
[Compare.]

4 The period of the sinusoid f(x) = a sin(bx + c) + d is 2π|b| .
[Formula.]

5 Hence, the period of the given sinusoid is 2π|1| = 2π.
[Compare.]

Hence the right answer is Option D

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