Question

B) On one rectangular coordinate system, show approximate radian values for one circle, as

well as the degree values for every 1/8 of one circle. (2 pts.)

Answer 1

(See explanation below for further details)

Explanation:

Any point in rectangular form can be described in terms of radius and angle of the circle. That is:

`P = (r\cdot \cos \theta, r\cdot \sin \theta)`

Since circunference is divided into 8 equal parts, the point can be modelled as:

`P = (r\cdot \cos (2\pi\cdot n)/(8), r \cdot \sin (2\pi\cdot n)/(8) )`

The approximate radian and degree values for one circle are:

Radians

`0 (0), (\pi)/(4) (0.785), (\pi)/(2) (1.571), (3\pi)/(4) (2.355), \pi (3.142), (5\pi)/(4) (3.925), (3\pi)/(2) (4.71), (7\pi)/(4) (5.495), 2\pi (6.280)`

Degrees

`0^(\circ), 45^(\circ), 90^(\circ), 135^(\circ), 180^(\circ), 225^(\circ), 270^(\circ), 315^(\circ), 360^(\circ)`