Question

A value of \theta between 0 and \pi that satisfies the equation sin^3(theta)-cos^3(theta) =1

Also if anyone knows a good site form me to improve my trigonometry I'd appreciate it.

Answer 1

\[\sin^3\theta-\cos^3\theta=(\sin\theta-\cos\theta)(\sin^2\theta+\sin\theta\cos\theta+\cos^2\theta)\\
=(\sin\theta-\cos\theta)(1+\sin\theta\cos\theta)\]
and I'm pretty sure there's a sum-to-product for this one.

Answer 2

Thanks man, I was putting it into wolfram but couldn't work out what I should be aiming for. pi/2 is the answer.

sing(pi/2)-cos(pi/2)(sin(pi/2)cos(pi/2)+1=1
=(1-0)(1*0+1)=1
1=1 qed.

Thanks again.

Answer 3

No prob. :)