Absolute Value of Trigonometric Function

From ProofWiki
Jump to navigation Jump to search


Let $\theta$ be an angle embedded in a Cartesian plane.

Let $\theta$ be such that the vertex of $\theta$ is located at the origin while one arm is coincident with the $x$-axis.

Let $\phi$ be the acute angle made by the other arm with the $x$-axis.

Let $f: \R \to \R$ be a trigonometric function.

Then $\size {\map f \theta}$ is equal to $\map f \phi$.

That is, a trigonometric function of an angle can be calculated by working out its quadrant to determine its sign, then using the equivalent value of what it is between $0$ and $90 \degrees$ to get its value.