Question

Express cos 7pi/3 as a trigonometric functions of an angle in quadrant 1 (picture provided)

Answer 1

`Cos ((\pi)/(3))`

Explanation:

To get the angle in the first quadrant, we need to subtract 2π from the angle given as many times we need UNTIL we get an angle that is between 0 degree and 90 degree (1st quadrant).

Let's start by subtracting 2π from the angle given:

`(7\pi)/(3)-2\pi\\=(7\pi -2\pi(3))/(3)\\=(7\pi - 6\pi)/(3)\\=(\pi)/(3)`

This angle is in the 1st quadrant, so we don't need to subtract 2π anymore. Thus we can write:

`Cos((7\pi)/(3))=Cos((\pi)/(3))`