## A Simple Trig Challenge

This is a fun and simple trigonometry challenge.

No calculators allowed!

Which of the following is the largest?

(a)  $\frac{\sqrt{3}}{2}$                           (b)  $sin (\frac{7\pi}{12})$

(c)  $sin (\frac{7\pi}{16})$                  (d)  $cos (\frac{\pi}{10})$

There are a couple of nice ways to solve this without using a calculator, and plenty of good ways to extend this question.

The real challenge is to come up with your own version of this problem!

1. Ahmed Gouda says:

I got C.

2. MrHonner says:

The question is how did you get it?

• Ahmed Gouda says:

The way I thought about it was sin pi/2 is 1. sin pi/3 is root 3 over 2. 7 pi over six is closer to one than pi over 3 so its larger than root 3 over 2. From there I just tried to find which is closest to 1. (D)pi over ten inserted into cos is pi over ten away which is larger then pi over 12 (B), and pi over sixteen is the smallest (c) so it seems to be the answer to me.