Trigonometric Identity- an equation involving trigonometric functions that can be solved by any angle
This page includes a PDF of all the trigonometric identites (below) and an explanation of each identity along with a derivation of four identities.
Trig Identities | |
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Fundamental Trig Identities
There are specific identities that are considered the building blocks that can form an infinite number of other identities. These equations are the most basic and important identities, and are true for any angle.
Quotient
- The ratio between sine and cosine
Reciprocal
- Relationship between the six core trigonometric functions: sine, cosine, tangent, secant, cosecant, and cotangent
- Expresses each function as a formula that makes it equal to one over another trig function
Pythagorean
- Holds true to any angle in question
- Relates to Pythagorean Theorem of a right triangle
Double Angle Trig Identities
These identities are used when we talk about 2Θ or other even multiples of Θ (as opposed to just Θ).
Power-Reducing Identities
This identity reduces second powers of trigonometric functions to first powers of sine, cosine, and tangent functions.
Sum and Difference Identities
These identities show just how different the algebra of functions can be from the algebra of real numbers. Pay close attention to each formula for sine, cosine, and tangent.
Half-Angle Identities
These identities can be used directly to find trigonometric functions of u/2 in terms of trigonometric functions of u.
Cofunction Identities
When C is the right angle in right △ABC, then angles A and B are complements. Therefore, the value of a function at A is the same as the value of its cofunction B (this always happens with complementary angles). This is why these identites have the name "co"functon- "co" stands for "compliment."
Even-Odd Identities
Every basic trig function is either odd or even. This usual function relationship leads to this fundamental identity.