Problems (1 Viewer)

[elizabethy]

hi ppl,

1) amplitude of sin squared x

2) region bounded by y=x^2 and y= 2-x^2 is rotated about the y axis. find the volume? ans is pi cubic units

3) Prove:

sinQ/1+cosQ=1-cosQ/sinQ

reply asap plzzzz

 

[Xayma]

1) Amplitude=1/2 (As max sine amplitude is 1, sine² amplitude is 1²/2 (as sine² is always ≥0) I think.

 

[smallcattle]

3)
SinQ / (1+CosQ) = (1-CosQ) / SinQ

Cross Multiply

Sin^2 Q = 1 - Cos^2 Q

Sin^2 Q + Cos^2 Q = 1

which is true

 

[acmilan]

1) Amplitude=1/2 (As max sine amplitude is 1, sine² amplitude is 1²/2 (as sine² is always ≥0) I think.

I remember doing this question for 4 unit maths as graphs was the only topic i did. The amplitude is actually 1 since you simply square the ordinates of sinx, the amplitude of sinx is 1 so the square of this is 1, meaning the amplitude is 1. All other values for sinx are < 1 and the square of a number < 1 is always < 1, hence the amplitude is 1

 

[Xayma]

But it oscillates around x=1/2.

It oscillates between 0 and 1.

And it takes as long to go from 1/2 to 1 as it does from 0 to 1/2. So the amplitude is 1/2.

 

[acmilan]

Woops sorry my mistake i had maximum point in my mind from that other thread