Cofunction identities

Definition

Cofunction identities are trigonometric identities that relate the functions of complementary angles. Specifically, these identities demonstrate that the value of a trigonometric function for an angle is equal to the cofunction of its complement.

5 Must Know Facts For Your Next Test

1. $\sin(90^\circ - \theta) = \cos(\theta)$ and $\cos(90^\circ - \theta) = \sin(\theta)$ are basic examples of cofunction identities.
2. Cofunction identities apply to tangent and cotangent: $\tan(90^\circ - \theta) = \cot(\theta)$ and $\cot(90^\circ - \theta) = \tan(\theta)$.
3. They also apply to secant and cosecant: $\sec(90^\circ - \theta) = \csc(\theta)$ and $\csc(90^\circ - \theta) = \sec(\theta)$.
4. These identities are useful for simplifying trigonometric expressions involving complementary angles.
5. Understanding cofunction identities can help in solving trigonometric equations and proving other trigonometric identities.

Review Questions

• What is the cofunction identity for $sin$?
• How does the cofunction identity relate to complementary angles?
• Provide a cofunction identity involving tangent and cotangent.

Related terms

Complementary Angles: Two angles that add up to $90^\\circ$.

Sum and Difference Identities: Formulas that express trigonometric functions of sums or differences of angles in terms of functions of individual angles.

Right Triangle Trigonometry: \text{A branch of trigonometry dealing with relationships between the sides and angles of right triangles.}