# 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.