Amplitude and period of the function?

Question

Hi.

I would like to know the answer to this question. Any help would appreciated.

What is the amplitude of the function

What is the exact period of f(x) (in radians)?

f(x) = - 8 sin(5*x + pi) .

just to note... I am talking about pi as in that "pi" that means the symbol pi which is 3.14....

Answer 1

y = a sin ( x )

Amplitude = | a |

y = -8 sin ( 5x + π )

Amplitude = | -8 | = 8

y = sin ( bx )

Period = 2π / | b |

y = -8 sin ( 5x + π )

Period = 2π / 5

Answer 2

Amplitude is the coefficient of the sine function so it is 8.

Period = 2pi/5 (5 comes from coefficient of x)

Answer 3

The amplitude is clearly 8 since the maximum amplitude of g(x) = sin(x) = 1, however I will use an angle for example:

I want to make  (5x + pi) equal to 3pi/2, so as to get sin(3pi/2) = -1

Hence I want to get 5x = pi/2

5x = pi/2

x = pi/10

5x + pi = 5*pi/10 + pi = the desired 3pi/2, so

(-8) * sin(3 pi/2) = (-8) * (-1) = 8

The amplitude is 8.   <<<<<

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Since we want to take the sine of 7pi/2 next instead of 3pi/2, 5x must increase by 2pi.

Hence 5x = 2pi

x = 2pi/5 is the exact period.