A list of trigonometric formulae and tables.

Trigonometric functions in polar coordinate form- radius $\rho$, azimuth $\phi$. Hypotenuse is $\rho$, adjacent is x and opposite is y.

$\sin \phi$ and $\cos \phi$ get the $y$ and $x$ components of $\rho$.

$\tan \phi$ and $\sec \phi$ get $y$ and $\rho$ from $x$.

$\cot \phi$ and $\csc \phi$ get $x$ and $\rho$ from $y$.

Trigonometric function values as a function of $\phi$. If the point is 0 or $\infty$, the $\pm$ and $\mp$ signs indicate the value of the function to either side of the specified point. Lower values of $\phi$ indicated by the sign on the top.

Transposed version.

Domain and range tables. Note that the range of the inverse trigonometric functions starts at either $-\frac \pi 2$ or 0, depending on the function.

Reciprocal and quotient identities.

Cofunction identities. All take the form $\operatorname{f} \left( \frac {\pi} {2} - {\phi} \right) = \operatorname{cof} {\phi}$ and vice versa.

Odd and even function identities. $\cos$ and $\sec$ are even. The rest are odd. %

Pythagorean identities. These cover all three sets of functions.

Trigonometric identities.

Sum and difference formulas.

Double angle identities.

Half angle identities.

Power reducing identities.

Spherical coordinates- radius $\rho$, inclination $\theta$, azimuth $\phi$.

Polar form of a complex number.

DeMoivre’s Theorem. $z^n$ is a complex number raised to the power of $n$.

The nth root of a number. There are $n$ complex roots for positive values of $n$. $k$ is used to calculate each root in turn.

Orthogonal decomposition.

Triangulation.

Angles from two locations- $\phi$, $\theta$. Baseline distance between locations- $\rho$. Shortest distance from baseline to target object- $y$. Distance along baseline from respective measuring points to point in front of target object- $x_\phi$, $x_\theta$. Distance from respective measuring points to target object- $d_\phi$, $d_\theta$. NOTE: $\phi$ and $\theta$ are interior angles.

Tangent line on circle of radius $\rho$ at angle $\phi$, simple rotations and mirrors.