sine and cosine

[kingjewel1]

hi there.

would you mind helping me a lil with this one.

it's sinx=1/2+cosx

i think its really easy to solve but i can never get a positive value for it.

i tried substituting Cos2x=1-2sin^2x

also tried it it with sec^2x=1+tan^2x

 

i know there's 1 positive and 1 negative value at least. between 0 and 2pi

thanks in advance

[matt grime]

there is a general formula for this:

 

p sin x + q cos x = k

 

let p=rcost and q = rsint for some numbers r and t, then q/p = tant, so we can find t, and p^2+q^2=r^2 so we can find r, then we've got

 

rcostsinx + rsintcosx=k

 

or

 

rsin(x+t)=k

 

so you can solve for x (note we've found r, t, and k was known)

 

 

now do it for

 

p=1, q=-1, k=1/2

[kingjewel1]

thanks Matt