Question

A point starts at the location (1.5,0) and moves counter-clockwise along a circular path with a radius of 1.5 units that is centered at the origin of an x-y plane. An angle with its vertex at the circle's center has a measure of θ radians and subtends the path the point travels. Let x represent the point's x-coordinate. (Draw a diagram of this to make sure you understand the context!)Complete the following statements.As θ varies from 0 to π/2, xvaries from  ____to  ____units.As θ varies from π/2 to π, x varies from  ____to  _____units.As θ varies from π to 3π/2, x varies from ____ to ____ units.As θ varies from 3π/2 to 2π, x varies from ____ to ____ units.

Answer 1

$\begin{gathered} a)\text{ 1.5 to 0} \\ b)\text{ 0 to -1.5} \\ c)\text{ -1.5 to 0} \\ d)\text{ 0 to 1.5} \end{gathered}$

We start with an image of the diagram as follows;

Now, we want to complete the statements

1. The first part talks about the first quadrant. As we can see, the value of x on the first quadrant ranges from the starting point x = 1.5 to the origin x = 0

2. The second part talks about the second quadrant. As we can see here, the value of x starts from the origin at x = 0 to x = -1.5

3. This talks about the third quadrant. The value of x here moves from x = -1.5 to x = 0

4. This talks about the fourth quadrant. The value of x here moves from x = 0 to x = 1.5