The Trig Calculator

For discussing Olympiad Level Algebra (and Inequality) problems
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Zawadx
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The Trig Calculator

Unread post by Zawadx » Thu Aug 04, 2016 7:50 pm

A calculator is broken so that the only keys that still work are the $ \sin$, $ \cos$, and $ \tan$ buttons, and their inverses (the $ \arcsin$, $ \arccos$, and $ \arctan$ buttons). The display initially shows $ 0$. Given any positive rational number $ q$, show that pressing some finite sequence of buttons will yield the number $ q$ on the display. Assume that the calculator does real number calculations with infinite precision. All functions are in terms of radians.

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Zawadx
Posts:90
Joined:Fri Dec 28, 2012 8:35 pm

Re: The Trig Calculator

Unread post by Zawadx » Thu Aug 04, 2016 7:52 pm

Hint to get started:
Draw a right angled triangle to try and understand the relationships between $\arcsin$, $\arccos$ and $\arctan$ with the trig functions.

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