Question

(a) Find an angle between 0 and 2pi that is coterminal with -pi/3(b) Find an angle between 0° and 360° that is coterminal with 690°.Give exact values for your answers.

Answer 1

We must find the coterminal angles of two angles.

1) The coterminal angle of θ = - π/3 between 0 and 2π. We have a negative angle in radians, to find its coterminal angle we sum 2π to it. The coterminal angle is:

`\theta+2\pi=-(\pi)/(3)+2\pi=-(\pi)/(3)+(6)/(3)\pi=(5)/(3)\pi\text{.}`

2) The coterminal angle of θ = 690° between 0° and 360°. We have a positive angle greater than 360°, to find its coterminal angle we substract 360° to it. The coterminal angle is:

`\theta-360^(\circ)=690^(\circ)-360^(\circ)=330^(\circ).`

Answers

1) 5/3 Pi

2) 330°