Question

Which of the following trig functions has an amplitude of 3?

(Note: The amplitude of a trig function is 1/2 the non-negative difference between the maximum and minimum value of the function.)

A. f(x)= 1/3 sin x

B. f(x)= sin 3x

C. f(x)= cos( 1/3 x)

D. f(x)= 3 cos x

E. f(x)= 3 tan x

Answer 1

Does it help if I say that sinx and cosx each go between -1 and +1 on the y axis?
Go through each of the transformations and note how they affect the function (draw a sketch if possible).

Answer 2

for any trig function the amplitude is the coefficient of the trig ratio

e.g. y = asin(bx) a is the amplitude 2pi/b is the period

Answer 3

the answers provided seem to differ from what you are trying to explain here

Answer 4

Also an important point: the amplitude IS NOT the difference between the maximum and minimum value, but it is HALF THE DIFFERENCE.

Answer 5

If f(x) = cosx takes y values between -1 and +1, then what happens when we multiply the whole function by 3? The whole function will scale up 3 times, going between -3 and +3.

Answer 6

so would it be A?

Answer 7

No it would be D. The transformation in A would divide all of the y values in the graph by 3, making the graph go between -1/3 and +1/3. Do you understand now?

Answer 8

um..

Answer 9

yes. thanx a lot! i'm not really good at trigonometry.

Answer 10

The important point to note is that multiplying a trig function on the outside (e.g: 3sin(x)) will stretch the y values, whereas multiplying a trig function on the inside (e.g: sin(3x)) will stretch the x values.

Answer 11

ok