Posted by **sh** on Friday, May 21, 2010 at 1:26pm.

Find the area between y=cosx and y=sinx from 0 to 2pi.

To find the zeros, I combined the equations cosx-sinx=0

What's next?

- Calculus -
**Damon**, Friday, May 21, 2010 at 4:57pm
Watch out.

Between 0 and 45 degrees, the cos is bigger than the sin.

Between 45 and 90, the sin is bigger than the cos.

In both sectors, there is area between them. The same in fact.

Therefore for quadrant 1, do 0 to pi/4 and double the result.

Then look at the other three quadrants.

- Calculus -
**Damon**, Friday, May 21, 2010 at 5:05pm
integral cos x dx from 0 to pi/4 = sin pi/4 - sin 0

= sqrt(2)/2

integral sin x dx from 0 to pi/4 = -cos pi/4 + 0 = -sqrt(2) /2

difference = sqrt 2

then integral from 0 to pi/2 = 2 sqrt 2

etc

- Calculus -
**Damon**, Friday, May 21, 2010 at 5:07pm
Oh, forgot you do not know where sin = cos

sure cos x - sin x = 0

1 -tan x = 0

tan x = 1

x = pi/4 (x = y at 45 deg)

## Answer this Question

## Related Questions

- Trig........ - I need to prove that the following is true. Thanks (cosx / 1-sinx...
- Pre-Calc - Trigonometric Identities Prove: (tanx + secx -1)/(tanx - secx + 1)= ...
- Trigonometry Check - Simplify #3: [cosx-sin(90-x)sinx]/[cosx-cos(180-x)tanx] = [...
- Math - Pre- Clac - Prove that each of these equations is an identity. A) (1 + ...
- Trigonometry. - ( tanx/1-cotx )+ (cotx/1-tanx)= (1+secxcscx) Good one! ...
- maths - trigonometry - I've asked about this same question before, and someone ...
- Math - Verify the identity . (cscX-cotX)^2=1-cosX/1+cosX _______ sorry i cant ...
- Calculus - If y=3/(sinx+cosx) , find dy/dx A. 3sinx-3cosx B. 3/(sinx+cosx)^2 C...
- Precalculus/Trig - I can't seem to prove these trig identities and would really ...
- trigonometry - can i use factoring to simplify this trig identity? the problem ...

More Related Questions