Thread: Using sin,cos,tan formulas.

I have v = 1000sin@cos@tan(@/2)
and I need to rearrnge it to

v = asin^2(@) + bsin^4(@/2)
And hence find values a and b.

Tried using double angle formulas, but I'm having trouble. Thanks for the help!

Hello, classicstrings!

Is there a typo?
In the final form, aren't both angles ½θ ?

I have: .v .= .1000·sinθ·cosθ·tan(½θ)

and I need to rearrange it to: .v .= .a·sin²(½θ) + b·sin^4(½θ)

And hence find values a and b.

Identities
. - - . sinθ .= .2·sin(½θ)·cos(½θ)
. . . . cosθ .= .1 - 2·sin²(½θ)
. .tan(½θ) .= .sin(½θ)/cos(½θ)


We have: .v .= .1000 · sinθ · cosθ · tan(½θ)

. . . . . . . .v .= .1000 · 2·sin(½θ)·cos(½θ) · (1 - 2·sin²θ) · sin(½θ)/cos(½θ)

. . . . . . . .v .= .2000·sin²(½θ)·(1 - 2·sin²θ)

. . . . . . . .v .= .2000·sin²(½θ) - 4000·sin^4(½θ)


Therefore: .a = 2000, b = 4000


Edit: silly me . . . I had dropped a zero . . . sorry!

My error in forgetting the @/2.

Is there any chance that there is an error in your working?

I think you left out one zero in 1000, so a = 2000, and doesn't b = negative 4000? Thanks!