You could just calculate cos(2θ) = cos(2arcsin(3/4)), which is -1/8.

~Gata.

Well, I admit I had to look up the double angle formulas, to refresh my memory, but oh well.

cos(2*a)=cos^2(a)-sin^2(a)=(cos^2(a)+sin^2(a))-2*sin^2(a)=1-2*sin^2(a)=1-2(sin(a))^2

Since arcsin(3/4)=a, then sin(a)=3/4 and you can plug that into cos(2*a)=1-2(sin(a))^2.

My way is significantly more convoluted than Gata's, but it avoids having to calculate nasty arcsines and cosines. >=3

Alrighty, thanks. Should've known that one.

I wish I was smart enough to understand the question.

Well, I admit I had to look up the double angle formulas, to refresh my memory, but oh well. :Pcos(2*a)=cos^2(a)-sin^2(a)=(cos^2(a)+sin^2(a))-2*sin^2(a)=1-2*sin^2(a)=1-2(sin(a))^2Since arcsin(3/4)=a, then sin(a)=3/4 and you can plug that into cos(2*a)=1-2(sin(a))^2.My way is significantly more convoluted than Gata's, but it avoids having to calculate nasty arcsines and cosines. >=3

I really have to refresh those. I bet or hope they look more confusing on the screen than they are on the screen, though.

Calculate nasty arcsines and cosines? Here we simply type it into the pocket calculator and voilà. Way faster than your formula.

~Gata.

I really have to refresh those. I bet or hope they look more confusing on the screen than they are on the screen, though.

 

Calculate nasty arcsines and cosines? Here we simply type it into the pocket calculator and voilà. Way faster than your formula. ~Gata.

The problem with that, was my calculator wasn't giving me easy values to work with. It would just say:

cos(2sin^-1(3/4))

It wouldn't evaluate it out.

What calculator are you using? Some are programmed to give exact answers when you hit ENTER and can be persuaded into giving approximations (decimals) by use of a secondary button in conjunction with ENTER.

I've got a TI-89. It can do approximations, but my professor wants exact answers.

TI-89 BROS UNITE! :3

We use CASIO fx-85 ES here. They give you exact values (when there are) and approximate values.

~Gata.

MY BRAIN

IT WEEPS