# Thread: double - angled formulas

1. ## double - angled formulas

Hey everyone!,

If anyone could help me with this, with explanation that would be great, thanks

(i) Using an appropriate double-angle formula, express sin(4θ) in
terms of sin(2θ) and cos(2θ).

formulas, derive the formula
sin(4θ) = 4 sin θ cos3 θ − 4 sin3 θ cos θ.

for (i) i've worked out (dunno if right)

sin(4θ) = using terms of sin(2θ) = 2sin(2θ)cos(θ)

using terms of cos(2θ) = 1 - 2sin^2(2θ)

but not sure how they would help for part (ii)

seems to be testing my skills in re-arranging the formulas

2. ## Re: double - angled formulas

Hi skeeter, had a look and this is what i come up with let us know,

2(2sintcost)(cos^2t-sin^2t) =

(2sintcost) * cos^2t = 2sintcostcos^2t = 2sintcos^3t

(2sintcost) * sin^2t = 2sintcostsin^2t = 2sin^3tcost

=

2(2sintcos^3t - 2sin^3tcost)

=

4sintcos^3t - 4sin^3tcost which is the answer, (broken down right?) thanks for letting us know about the (^)!

,

,

### 2sintcost formual

Click on a term to search for related topics.