http://i.imgur.com/pvhhgrA.jpg

How does that work? I've tried it with various values on the calculator and it's not equal. eg cos4 - 1 is not equal to -sin4 (if theta = 2). If neccesary, I can post the entire question. It concerns limits.

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- May 2nd 2013, 03:34 PMlukasaurusHow does cosx^2 -1 = -sinx^2? Q concerning limits.
http://i.imgur.com/pvhhgrA.jpg

How does that work? I've tried it with various values on the calculator and it's not equal. eg cos4 - 1 is not equal to -sin4 (if theta = 2). If neccesary, I can post the entire question. It concerns limits. - May 2nd 2013, 03:37 PMMarkFLRe: How does cosx^2 -1 = -sinx^2? Q concerning limits.
Are you squaring the trig. functions when you test with your calculator?

- May 2nd 2013, 03:54 PMlukasaurusRe: How does cosx^2 -1 = -sinx^2? Q concerning limits.
I've got an old fx-82. I don't have any option to square the actual trig function, but I should be able to square the x value right?

let theta = x (because it's quicker to write)

so let x = 2

cos^2(x) -1 = cos4 -1 = -0.002

-sin^2(x) = -sin4 = -0.07

No idea what I am doing wrong..

edit: Actually, it should be (cosx)^2 right? not what I am doing. I think I got it. - May 2nd 2013, 05:32 PMHallsofIvyRe: How does cosx^2 -1 = -sinx^2? Q concerning limits.
You may be confusing $\displaystyle cos^2(x)$ with $\displaystyle cos(x^2)$.

If x= 2 radians, then cos(x)= cos(2)= -0.416147 so that $\displaystyle cos^2(2)= 0.17318$.

But $\displaystyle cos(x^2)= cos(4)= -0.6536436$.