# Expression in Terms of Theta

• Apr 30th 2009, 10:04 AM
ThaBeretta
Expression in Terms of Theta
A crate weighing $\displaystyle w$ pounds sits on a ramp positioned at an angle of $\displaystyle \theta$ with the horizontal. The forces acting on this crate are modeled by the equation $\displaystyle Mw cos \theta = w sin \theta$ , where $\displaystyle M$ is the coefficient of friction. What is an expression for $\displaystyle M$ in terms of $\displaystyle \theta$ ?

a) $\displaystyle M = tan \theta$

b) $\displaystyle M = sec \theta$

c) $\displaystyle M = cot \theta$

d) $\displaystyle M = csc \theta$
• Apr 30th 2009, 10:09 AM
e^(i*pi)
Quote:

Originally Posted by ThaBeretta
A crate weighing $\displaystyle w$ pounds sits on a ramp positioned at an angle of $\displaystyle \theta$ with the horizontal. The forces acting on this crate are modeled by the equation $\displaystyle Mw cos \theta = w sin \theta$ , where $\displaystyle M$ is the coefficient of friction. What is an expression for $\displaystyle M$ in terms of $\displaystyle \theta$ ?

a) $\displaystyle M = tan \theta$

b) $\displaystyle M = sec \theta$

c) $\displaystyle M = cot \theta$

d) $\displaystyle M = csc \theta$

Divide through by $\displaystyle wcos(\theta)$:

$\displaystyle M = \frac{wsin(x)}{wcos(x)}$

w will cancel out and what does sin(x)/cos(x) equal (Wink)
• Apr 30th 2009, 10:14 AM
ThaBeretta
$\displaystyle M = \frac{wsin(x)}{wcos(x)}$is equal to $\displaystyle tan \theta$ . Thus the answer is choice "a". Thanks again! (Wink)