How do you find the amplitude and period of f(x) = - 8 sin(5*x + pi) ?

1 Answer
Jul 25, 2015

Amplitude = 8
Period = (2pi)/5

Explanation:

f(x) = -8 sin( 5x + pi )
=> f(x) = 8 (-sin( 5x + pi ) )
=> f(x) = 8 sin( 5x + cancel(pi) - cancel(pi) ) (Since -sin(x) = sin( x - pi )
=> f(x) = 8 sin( 5x )

Since | sin(x) | <= 1 forall x , the amplitude of f(x) is 8.

Now, for the period, notice the following:
f( x + (2pi)/5) = 8 sin( 5 ( x + (2pi)/5 ) ) = 8 sin( 5x + 2pi ) ) = 8 sin( 5x ) = f(x)

Thus the period of f(x) is (2pi)/5 .

Note: In general, for any sinusoidal function of the form sin(nu x) or cos(nu x) , the period is (2pi)/nu . Here nu is the frequency multiplication factor. In this particular case, nu = 5 .