Analytic Trigonometry
Lessons in this chapter
About Analytic Trigonometry
Analytic Trigonometry covers the identities that let you rewrite, simplify, and prove trigonometric expressions.
Basic Trigonometric Identities introduces the fundamental relationships between the trig functions, before Simplifying and Proving Equivalence of Trigonometric Expressions uses them to rewrite and verify more complex expressions.
Sum and Difference Identities closes the chapter with the formulas for the sine, cosine, and tangent of a sum or difference of two angles.
The three lessons, Basic Trigonometric Identities, Simplifying and Proving Equivalence of Trigonometric Expressions, and Sum and Difference Identities, each open as a worksheet worked in the page. Every problem is scored as it is answered, so an identity applied in the wrong direction is caught at that question. Free to practice online.
Frequently asked questions
Basic Trigonometric Identities covers the Pythagorean, reciprocal, quotient, and even and odd identities, the small set everything else is built from. Simplifying and Proving Equivalence of Trigonometric Expressions uses them to rewrite one expression as another, which is what most of the chapter's problems come down to. Sum and Difference Identities closes with the formulas for the sine, cosine, and tangent of a sum or difference of two angles. This sits in Functions (F) in the high school Common Core.
The Pythagorean identity (sin²θ + cos²θ = 1) and the reciprocal and quotient identities relate the six trig functions to each other.
Simplify one side of an expression using known identities until it matches the other side exactly, or reduce both sides independently to the same simplified form.
The sum and difference identities give the sine, cosine, or tangent of a sum or difference of two angles in terms of the individual angles’ sine, cosine, and tangent values.
They let you find an exact trigonometric value for an angle that isn’t a standard angle, by writing it as a sum or difference of two standard angles.
Treating sin(A + B) as sin(A) + sin(B): the sum and difference identities do not distribute across the trig function this way, and the actual formulas must be used.