Question

How can i find the period and amplitude of y=sin^2x with out graphing it?

Answer 1

Period = 360 / (coefficient of x) if x is in degree
Period = 2pi / (coefficient of x) if x is in radians
Amplitude is the coefficient of the sine function

Answer 2

Oops forgot about the square

Answer 3

:P

Answer 4

The amplitude is the same but the period is halfed.

Answer 5

If the power is even, the period is cut in half, if the power is oddthe period remains the same. And as TURITW said, you also factor in the angle. The period is 2pi divided by the coefficient of x. Since the coefficient of x for you is 1 and the power is even, your period is pi.

Answer 6

okay thanks! so you only half the period when it is raised to an even power?

Answer 7

Yes

Answer 8

If it's an even power, the graph is forcedto avoid negative values, so it bounces back up at pi and starts over. If the power is odd then negative values can exist and the graph continues on it's normal period.

Answer 9

and for the amplitude, the answer says that it is 1/2. but if the amplitude remains the same for this problem how come the amplitude is not 1?

Answer 10

Well we didn't discuss amplitude, lol.

Answer 11

Hm? The amplitude should be 1

Answer 12

@ psymon: TURITW said that in the beggining lol
and my answer sheet says it's 1/2

Answer 13

y = sin^2 x
Since -1 <= sin x <= 1, sin^2 x <= 1
y = sin^2 x <= 1, which means the highest possible value of y /amplitude is 1

Answer 14

hmm then I'm not sure why it says 1/2 but thanks!