# Homework Help: Sketching A Graph Using Differentiation

1. Sep 5, 2010

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

I don't understand how they get from step 4 to step 5. Wouldn't you factor a cos x out of the brackets then have $$(\cos x)(1-\frac{1}{6})$$ to the left of the brackets. Then you can multiply the $$(1-\frac{1}{6})$$ inside the brackets.However that would yield $$[\frac{5}{6}+\frac{10}{3}\sin^2x]$$ I dont understand how they are getting 1- (1/6) times the stuff inside the brackets.

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Last edited: Sep 5, 2010
2. Sep 6, 2010

### Coto

$$\cos x - \frac{1}{6}[(1-2\sin^2 x)\cos x - 2\sin^2 x\cos x]$$

$$= \cos x - \frac{1}{6}[ \cos x (1-2\sin^2 x - 2\sin^2 x) ]$$

$$= \cos x - \frac{1}{6} \cos x(1-2\sin^2 x - 2\sin^2 x)$$

$$= \cos x [ 1 - \frac{1}{6}(1-2\sin^2 x - 2\sin^2 x) ]$$