# double or half angle formula to solve

• Feb 7th 2009, 02:15 PM
guardofthecolor4ever
double or half angle formula to solve
don't know how to use double or half angle formula to solve the equation:

sin2x+cosx=0

in the interval [0, 2pi) and the answers are pi/2, 7pi/6, 3pi/2, 11pi/6
• Feb 7th 2009, 02:21 PM
mr fantastic
Quote:

Originally Posted by guardofthecolor4ever
don't know how to use double or half angle formula to solve the equation:

sin2x+cosx=0

in the interval [0, 2pi) and the answers are pi/2, 7pi/6, 3pi/2, 11pi/6

Substitute $\sin (2x) = 2 \sin x \cos x$.

Now factorise the resulting expression. Now apply the null factor law to get two simple trig equations that you need to solve over the given interval:

$\cos x = 0$

$2 \sin (x) + 1 = 0$
• Feb 7th 2009, 02:32 PM
guardofthecolor4ever
thanks!