Right Triangle Trigonometry Definitions

Given triangle ABC,

There are six possible side ratios named: Sine, Cosine, Tangent, Cosecant, Secant, and Cotangent.

The Pythagorean theorem applies,

Special 30-60-90 triangle:

Special 45-45-90 triangle:

Special Trig Function Values:

Pythagorean triples (primitives) with c ≤ 100:

Note: (6, 8, 10) is not a primitive because it is a multiple of (3, 4, 5).

Trigonometric functions of special angles in classic table form:

Area and Perimeter of Common Shapes

Triangles:

Area given all sides (SSS) - Heron's Formula

Heron of Alexandria:

Rectangles and Squares:

  

Parallelograms:

 

 Trapezoids:

 

Circles:

Polygons

Convex Regular Polygons (n-gons)

• Pentagon – n = 5 sides
• Hexagon – n = 6 sides
• Heptagon – n = 7 sides
• Octagon – n = 8 sides
• Nonagon – n = 9 sides
• Decagon – n = 10 sides

Perimeter and Area

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General Triangles

Given the general triangle ABC,

Area (use radians)

Area given all sides (SSS) - Heron's Formula

Law of Sines (AAS, ASA, or ASS)

Law of Cosines (SAS or SSS)

Law of Tangents

Mollweide's Formulas,