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In trigonometry, how can we find the sine/cosine of an angle larger than 90 degrees, if sine and cosine only work for right triangles? [duplicate]

In trigonometry, how can there be angle thetas larger than 90 degrees, if sine and cosine only work for right triangles? I realize what we do is that we take the sine or cosine of the angle ...
24 views

In Unit circle, in second quadrant, why is X taken negative? [duplicate]

Cos theta = base / hypotenuse Base and hypotenuse are lengths, so they should always be positive. So why is cos 3π / 4 negative ?
56k views

What is the most elegant proof of the Pythagorean theorem? [closed]

The Pythagorean Theorem is one of the most popular to prove by mathematicians, and there are many proofs available (including one from James Garfield). What's the most elegant proof? My favorite ...
38k views

How can I understand and prove the “sum and difference formulas” in trigonometry?

The "sum and difference" formulas often come in handy, but it's not immediately obvious that they would be true. \begin{align} \sin(\alpha \pm \beta) &= \sin \alpha \cos \beta \pm \cos \alpha \...
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Why is $n$ divided by $n$ equal to $1$?

I've understood how to apply this operation for many years but I recently was reminded that: $n^0 = 1$ Which in high school I accepted and just "solved for", but I'm now curious. Why is that true? ...
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Different definitions of trigonometric functions

In school, we learn that sin is "opposite over hypotenuse" and cos is "adjacent over hypotenuse". Later on, we learn the power series definitions of sin and cos. How can one prove that these two ...