Nice Question (1 Viewer)

[Kutay]

" Solve cosx + root 3 sinx = 0.5 for 0 <(orequal) x <(orequal) , answer the 3 sig figures"

i am pretty sure fro this question i got to use like not the T-method because cant work it out but that other way anyhow anyone know how to do it step by step?

 

[Slidey]

Divide both sides by two:
1/2 * cosx + sqrt3/2 * sinx = 1/4
By inspection:
cos(pi/3) * cosx + sin(pi/3) * sinx = 1/4
cos(x-pi/3)=1/4
x=2.36 rad
I think. I'm not good with significant figures.

I haven't done transformations for a while, so I'm sorry, but somebody else will have to help you there.

 

[Trev]

By transformation:
acostheta + bsintheta = rcos(theta - alpha) where r = (a² + b²)^1/2 and alpha = b/a.
Therefore, in this case
r =(1² + (3^1/2)²)^1/2 = (1 + 3)^1/2 = 2
tanalpha = (3^1/2)/1
angle alpha = 60 degrees
= 2cos(theta - 60) = .5
cos(theta - 60) = .25
theta - 60 = 75°31', 284°29'

theta = 135°31', 344°29'