# Calculus Summer Assignments

hotrocks007
I'm taking Calculus next year and over the summer I have some assignments.
This one is due in a couple of hours, so any help would be appreciated!

If cos2t=1/3 and *0<_ 2t <_ pie, find cost. t=theta *less than or equal to

I dont know how to use the identities to help me.

Gold Member
MHB
Well....

$$\cos{(2\alpha)} = 2\cos^2{(\alpha)}-1$$

Plug that in and post when you make progress.

hotrocks007
ohh, costheta=sqrt(6)/3
?

Gold Member
MHB
$$2\cos^2{(\alpha)}-1 = \frac{1}{3}$$

$$2\cos^2{(\alpha)}=\frac{4}{3}$$

$$\cos^2{(\alpha)}=\frac{2}{3}$$

Can you finish from here?

hotrocks007
oh yes thanks!

I'm not sure how to simplify it down, and how to distribute the ^2 once it has been plugged in.
x^2 + y^2 +3x=0 when x=rcostheta and y=rsintheta

Nylex
Remember that $\sin^2 x + \cos^2 x = 1$. These questions don't seem to have anything to do with calculus, they just seem to be trigonometry.

Gold Member
MHB
$$(r\cos{\theta})^2 + (r\sin{\theta})^2+3(r\cos{\theta})=0$$

$$r^2\cos^2{(\theta)}+r^2\sin^2{(\theta)}+3(r\cos{\theta})=0$$

Do you see the trig identity coming in?

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hotrocks007
the Pythag. Identity? Would you have to plug in rcostheta with the 3x?

Gold Member
MHB
I should have plugged that in earlier. But no, that's not where the identity comes in.

I'll give you my last hint to this problem.

$$r^2\cos^2{(\theta)}+r^2\sin^2{(\theta)}+3(r\cos{\theta})=0$$

$$r^2(\cos^2{\theta}+\sin^2{\theta})...$$

hotrocks007
OH! thanks!!!!!

hotrocks007
when you distribute the 3, would it be 3rcos3theta? or do you just not distribute the 3 to the cos?

Gold Member
MHB
$$3r\cos{(\theta)}$$