Trigonometry Formulae - Part 1

Geometry Level 3

If the ending ray of angle $\displaystyle α$ is in Second quadrant, which quadrant can't the ending ray of $\displaystyle \frac{α}{3}$ be in?

Third quadrant Second quadrant First quadrant Fourth quadrant

1 solution

Chris Lewis
May 20, 2019

It's a bit easier to think about what happens to the quadrants under the map $\theta \to 3\theta$ :

From these diagrams we see that only the third quadrant contains no $\theta$ that maps to the second quadrant under tripling.