Okay, I feel like a retard. Did this shit like a year ago, but I need to recap and can't remember how to do this for the life of me (should be very simple).

Find the values of sin(x) and cos(x) when cos(2x) is 1/9

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Posts: 11095

Okay, I feel like a retard. Did this shit like a year ago, but I need to recap and can't remember how to do this for the life of me (should be very simple).

Find the values of sin(x) and cos(x) when cos(2x) is 1/9

Find the values of sin(x) and cos(x) when cos(2x) is 1/9

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dave

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dave

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Posts: 1906

ti 89

solve(cos^(-1)(1/9)=2x,x)

boom

Posts: 100

Non-calculator way:

Posts: 100

Oops, accidently hit enter. Cos2x=cos^2x-sin^2x Also cos2x=2cos^2x-1. And cos^2x=1-2sin^2x Set the second two both equal to 1/9, should get cosx=square root of 5/9 and sinx=2/3. Substitute answers back into first equation to check answers. 1/9= 5/9-4/9

Posts: 2600

SOHCAHTOA

Cos (2x) = 1/9 = adjacent/ hypotenuse

2x= 1/9, x= (1/9)/2 =1/18

x= 1/18

sin (1/18) = .0556

cos (1/18)= .9985

hope that helps, since I just basically did that whole thing for you. I'm a math nerd.

Cos (2x) = 1/9 = adjacent/ hypotenuse

2x= 1/9, x= (1/9)/2 =1/18

x= 1/18

sin (1/18) = .0556

cos (1/18)= .9985

hope that helps, since I just basically did that whole thing for you. I'm a math nerd.

Posts: 30792

answers are correct

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Posts: 2600

Did you not see where I said I'm a math nerd! YOU should know better Jamie!

Posts: 30792

I came here to write the same thing, but just backed you up. And that makes two of us kimber :)

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Posts: 100

How is that correct? The cos of cos2x cannot just disappear, you'd have to take the cosine inverse to get rid of it. So to solve for x, it would be

cos2x=1/9

cos^-1 (cos2x)=cos^-1 (1/9)

2x=cos^-1 (1/9)

x=cos^-1 (1/18)

But the problem can easily be solved without a calculator using double angle identities, so why not just do it that way and get "nice" numbers?

cos2x=1/9

cos^-1 (cos2x)=cos^-1 (1/9)

2x=cos^-1 (1/9)

x=cos^-1 (1/18)

But the problem can easily be solved without a calculator using double angle identities, so why not just do it that way and get "nice" numbers?

Posts: 1906

lol not even close

Posts: 2600

lol you are right, I completely forgot afterwards that cosx does not equal cos2x/2

I fail, maybe I should go back to high school

I fail, maybe I should go back to high school

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