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!