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Calculus Summer Assignments

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.
:confused:
Please help!
 
788
0
Well....

[tex]\cos{(2\alpha)} = 2\cos^2{(\alpha)}-1[/tex]

Plug that in and post when you make progress.
 
ohh, costheta=sqrt(6)/3
?
 
788
0
[tex]2\cos^2{(\alpha)}-1 = \frac{1}{3}[/tex]

[tex]2\cos^2{(\alpha)}=\frac{4}{3}[/tex]

[tex]\cos^2{(\alpha)}=\frac{2}{3}[/tex]

Can you finish from here?
 
oh yes thanks!

how about this one.

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
 
551
1
Remember that [itex]\sin^2 x + \cos^2 x = 1[/itex]. These questions don't seem to have anything to do with calculus, they just seem to be trigonometry.
 
788
0
[tex](r\cos{\theta})^2 + (r\sin{\theta})^2+3(r\cos{\theta})=0[/tex]

[tex]r^2\cos^2{(\theta)}+r^2\sin^2{(\theta)}+3(r\cos{\theta})=0[/tex]

Do you see the trig identity coming in?
 
Last edited:
the Pythag. Identity? Would you have to plug in rcostheta with the 3x?
 
788
0
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.

[tex]r^2\cos^2{(\theta)}+r^2\sin^2{(\theta)}+3(r\cos{\theta})=0[/tex]

[tex]r^2(\cos^2{\theta}+\sin^2{\theta})...[/tex]
 
OH! thanks!!!!!
 
when you distribute the 3, would it be 3rcos3theta? or do you just not distribute the 3 to the cos?
 
788
0
[tex]3r\cos{(\theta)}[/tex]
 

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