How Do You Simplify Trigonometric Expressions?

# How Do You Simplify Trigonometric Expressions?

Simplifying trigonometric expressions is a matter of understanding the circles and triangles upon which trigonometry is based. While much of the simplification can be done geometrically, knowledge of trigonometric identities will allow an algebraic solution.

Every time you see sin x or cos x, know that x can be replaced with x-2? or x+2? (if in radians) or x-360 or x+360 (if in degrees) with no change in value. Sine and cosine are periodic functions, meaning that their values repeat every 2? or 360 degrees. Further, when you see tan x or cot x, it is periodic with repeating values every ? radians or 180 degrees, so x can be replaced with x+? or x-?, for example, sin 7? = sin 5? = sin 3? = sin ? = 0.

2. Use Pythagorean identities

When some terms are difficult to simplify, using these identities can yield a different result that is more manageable : sin^2 x + cos^2 x = 1 tan^2 x + 1 = sec^2 x cot^2 x + 1 = csc^2 x Keep in mind that these equations can also be manipulated to fit what you need. What does sec^2 x - 1 equal?