Tangents to polar curves

The  exercise appears under the Differential calculus Math Mission. This exercise practices practices converting tangents to polar curves.

Types of problems
There are three types of problems in this exercise:
 * 1) Determine the x-intercept: This problem has a tangent line drawn to the polar curve ___ at the point where _ = ___. User is asked to find the x-intercept of that line rounded to the nearest 0.001.
 * 2) Determine whether each one is positive, negative, or zero at point __: This problem has a graph of a four petal flower, and given the four instantaneous rates of change listed in the table below, user is asked to determine whether each one is positive, negative, or zero at point __.
 * 3) Determine the exact slope of the tangent line to the polar curve where __ = __ and __ = __: This problem asks user to find the exact slope of the tangent line to the polar curve where __ = __ and __.

Strategies
Basic knowledge of tangents and polar curves is required for this exercise.
 * 1) User first needs to find $$\frac{dy}{dx}$$space for the curve, recalling that for a polar curve
 * 2) For a polar curve, $$x=r\cos\theta$$ and $$y=r\sin\theta$$

Real-life Applications

 * 1) Problems like this will appear on standardized tests, such as the SATs and ACTs.