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Differentiating watch

1. I have got so much maths homework to do =(.. and i have just come across this question i can't do:

y=sin^3x have five stationary points between -pie and pie.
Find the five stationary points.

I've worked out dy/dx to be: cosx x 3(sin x)^2
and now im stuck

Can anyone help?

xxx
2. You know that the stationary points are when ; so you need to solve . There should be 5 solutions for x in between and . Then plug those values back into the original equation to find y.
3. yeah i know that.. but i just dont know what the solutions would be:| x
4. solve cos x = 0 and sin^2 x = 0
5. Ah. Treat it like you would a factorised quadratic and solve it separately:
and
6. i mite sound like im being stupid but how would i solve cosx=0 ? x

7. therefore one solution is

If you put into your calculator, you should get . That's one of the answers.
Do you know what the graph of y=cosx looks like? Sketch it for x between and and use the symmetries of the graph to work out the other solutions. (You should get one other solution.)

Do the same for , but square root it first to make it simpler. There should be three solutions for this one.
8. square root what?
9. Both sides of the equation, so it becomes .
It'll work with , but most people are more familiar with sinx=0.

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Updated: August 24, 2008
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