Question

Determine the length of the arc (in radian measure) and the measure of the angle (in radian degree measures) generated by a point that starts (1,0)and terminates at the following:

1. Positive x-axis

2. Negative x-axis

3.Positive y-axis

4.Negative y-axis

Answer 1

The circumstance $(2πr)$ of a unit circle is $2π(1) = 2π.$

1. An angle starting at Cartesian point $(1,0)$ and terminating at the positive $x$ - axis would represent angle of $2\pi$ radians, this would be complete circumstance arc length, that is $2\pi$ radians. We can consider the angles of $2\pi n$ radian, $n\in \N$ and the corresponding lengths of arc of $2\pi n$ unis of length.

2. An angle starting at Cartesian point $(1,0)$ and terminating at the negative $x$ - axis would represent angle of $\pi$ radians, this would be complete the half of circumstance arc length, that is $\pi$ radians. We can consider the angles of $\pi+2\pi n$ radian, $n\in \N$ and the corresponding lengths of arc of $\pi+2\pi n$ unis of length.

3. An angle starting at Cartesian point $(1,0)$ and terminating at the positive $y$ - axis would represent angle of $\pi/2$ radians, this would be complete the 1/4 of circumstance arc length, that is $\pi/2$ radians. We can consider the angles of $\pi/2+2\pi n$ radian, $n\in \N$ and the corresponding lengths of arc of $\pi/2+2\pi n$ unis of length.

4. An angle starting at Cartesian point $(1,0)$ and terminating at the negative $y$ - axis would represent angle of $3\pi/2$ radians, this would be complete the 3/4 of circumstance arc length, that is $3\pi/2$ radians. We can consider the angles of $3\pi/2+2\pi n$ radian, $n\in \N$ and the corresponding lengths of arc of $3\pi/2+2\pi n$ unis of length.