Need Math Help

[ß?µ£ §mµ®ƒ]

find the following trigonometric expression as an algebraic expression in terms of x show all work

sin (2arcsinx)-cos(2arccosx)

[FreakBaller12]

i am doign sign and cosign now. If you have a graphign calculator you should use that. I don't quite understand the problem you are trying to solve.

[ß?µ£ §mµ®ƒ]

it wants an algebraic expression simplified i think cause after im suppose to plug the answer into x to solve sin(2arcsinx) = cos(2arccosx)

[ScatterPlot]

sin (2arcsinx)-cos(2arccosx)

Haven't done strait trig in a while, so I can't remember what to do with the 2's, but the sin of the arcsin of something cancels. I.E. sin(arcsinX)=X. The problem wants you to get rid of the sines and cosines and all. Since there's no = sign I don't think you need to substitute. Just get rid of the 2's however you can and you can just cancel the trig parts. I think this is right. I know it works with log properties, but this could be different.

[gimp]

Originally posted by ß?µ£ §mµ®ƒ
find the following trigonometric expression as an algebraic expression in terms of x show all work

sin (2arcsinx)-cos(2arccosx)


sin (2arcsinx)-cos(2arccosx) = ? doesn't it have to equal something? If you got rid of the 2s, it would be x-x. I think the 2 messes it up though

[ScatterPlot]

It's an expression, not an equation, so I'm pretty sure it doesn't have to equal something. The 2's make it do something weird, and I can't remember how to get rid of them.

[deadeye9]

The best I can do is:

cos(2*arccos(x)) = 2*x^2 - 1

and

sin(2*arcsin(x)) = 2*x*sqrt(1 - x^2)

The first comes from the trig identity:
cos(2y) = 2*cos^2(y) - 1

The second comes from the trig identity:
sin(2y) = 2*sin(y)cos(y), therefore
sin(2*arcsin(x)) = 2*x*cos(arcsin(x))

Let y = ArcSin(x). We seek Cos(y). Then

Sin(y) = x
1 - (Sin(y))^2 = 1 - x^2
(Cos(y))^2 = 1 - x^2
Cos(y) = sqrt(1 - x^2)

I got that last part from:
http://mathforum.org/epigone/alt.math.undergrad/kaxrimwo/87fojb$ti$1@nnrp1.deja.com

[splatattack33]

wow glad im still in 9th grade math

[sharpshooter1286]

wow glad im still in 9th grade math