1
$\begingroup$

Is there a way to solve for x where $\operatorname{trig function}(x) = \mathrm{constant}$ and where the domain is such that the function has an inverse.

For example,

$\begin{align*}\sin x &= \sqrt3 / 2,\\ \cos x &= -1,\\ \tan x &= 1/\sqrt3\end{align*}$

  • 1
    @Matt, [De Moivre's formula](http://en.wikipedia.org/wiki/De_Moivre%27s_formula) is the source of a connection between trigonometry and roots. It's not completely direct though, and the question of which angles it works for is surprisingly nontrivial (and is one of the prime motivations for Galois theory).2011-09-23

1 Answers 1

2

All of the examples that you give (now that we have changed the first constant to $\sqrt{3}/2$ ) are values on the unit circle.
When you first learn about this, you'll be asked which angles satisfy the equation:

TrigFunction(angle) = constant, where the trig functions are:

sin, cos, tan, csc, sec, cot, and the constants are quotients involving:

$\pm \{0, \frac{1}{2}, \frac{\sqrt{2}}{2}, \frac{\sqrt{3}}{2}, 1 \} $

  • 1
    (This might not have been too long for a comment, but I needed the compiler to help with my LaTexing)2011-09-23