Question

How does the ideal mechanical advantage (IMA) of an inclined plane vary

with the angle 𝜃 of the plane; that is, what trigonometric function of 𝜃 gives the value of IMA?

Answer 1

1) Write the expression for IMA, which is the ration of length of effort over height:

$$IMA=\dfrac{L}{H}.$$

2) Notice that the height can be expressed in terms of length:

$$H=L\sin\theta→IMA=\dfrac{L}{L\sin\theta}=\dfrac 1{\sin\theta}=\csc\theta.$$