# Why does this always equal $1$?

One of my friends told me this. Take a calculator and continuously input $\cos\tan\sin\cos\tan\sin\ldots$ any number of times you want and finally in the place of the angle measure place any value of your choice (ANY). The result the calculator told me 99 out of 100 times was 1. And the one time it didn't tell me 1, it told me 0.9999999. Why does this happen?

• Nice!!! To make it easier on readers who are using Windows calculator, you should give the instructions "in reverse": Input any value you like, then click sin, then click tan, then click cos. +1. Mar 5, 2015 at 18:54
• The answer is pretty obvious, BTW. Sin brings it to a value between $-1$ and $1$. Tan therefore brings it to a value close to $0$, and Cos therefore brings it to a value close to $1$. Mar 5, 2015 at 18:55
• It apparently only works in degrees. Mar 5, 2015 at 18:57

## 1 Answer

Try switching your calculator to radians-what's happening is that when it's in degrees and you take the sine of anything it's going to be between 1 and -1. Then if you take the tangent of something between -1 and 1 degrees, it's going to be very close to 0. When you take the cosine of something very close to 0, it's going to be very close to 1. And then this process repeats. If you do it in radians, it's a bit more sporadic.

• At least give some credit to my comment on the question :) Mar 5, 2015 at 19:00