# Block pull, Problems with trig to isolate for theta.

1. Jul 28, 2013

### cambo86

1. The problem statement, all variables and given/known data

What value(s) of θ will result in the block being accelerated 9.0m/s2 to the right?

2. Relevant equations
ƩFx = max
N = mg - P sin(θ)

3. The attempt at a solution
P cos(θ) - μkN = max
P cos(θ) - μk(mg - P sin(θ)) = max
P cos(θ) + μk P sin(θ) = max + μkmg
cos(θ) + μk sin(θ) = (1/P)(max + μkmg)

From here I can't find a trig identity that will help me isolate for theta.

2. Jul 28, 2013

### voko

$a \cos \theta + b \sin \theta = r (\cos \alpha \cos \theta + \sin \alpha \sin \theta)$, where $r = \sqrt {a^2 + b^2}$ and $\cos \alpha = a/r , \ \sin \alpha = b/r$.

Last edited: Jul 28, 2013
3. Jul 28, 2013

### Staff: Mentor

Another approach is to replace one of the trig functions (say cos) using the identity sin2 + cos2 = 1. Rearrange the resulting expression so that squaring both sides eliminates the square root.