Core Trigonometry

This page provides reference material for the most common concepts for precalculus trigonometry.
It is meant as a handy supplement while doing homework or studying for exams.


GOAL: practice the use of these formulas frequently enough to feel comfortable about deciding
which ones to use at particular times, based on whatever trig problem you may be trying to solve.

Degrees and Radians:

The Unit Circle


The Core Formulas:

The Core Derivations:

Using the Unit Circle, you can derive sin, cos, or tan from x, y, and r (see unit circle above),
where r will equal 1, because that's what the word "unit" means in Unit Circle.

NOTE: r will not equal 1 whenever you are doing harder trig that extends beyond the Unit Circle.

The Core Quotients

The Core Reciprocals


Pythagorean Trigonometry:

The Core Pythagorean Formulas

The Typical Pythagorean Variations


The Core Graphs:

The Essential Sinusoidal Graphs



The Sinusoidal Equation Template

Based on this General Equation for sinusoidal equations, you can alter and transpose many of
the basic features (listed below equation) of the prototypical graphs that appear above.


The Composite Formulas:

Composite Angle Formulas

Double Angle Formulas

Half Angle Formulas


The Odd/Even Formulas:

Odd & Even Function Formulas


The Inverse Trig Rules:

These rules establish the periodicity of your answer when you use an inverse trig function to find your way back to an angle.

Using Radians

Using Degrees