In trigonometry, cofunctions are pairs of trigonometric functions where the function of an angle is equal to the cofunction of its complement. For example, $\sin(90^\circ - \theta) = \cos(\theta)$ and $\tan(90^\circ - \theta) = \cot(\theta)$.
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1. Cofunction identities are crucial for simplifying trigonometric expressions involving complementary angles.
2. The main pairs of cofunctions are sine-cosine, tangent-cotangent, and secant-cosecant.
3. The identity $\sin(90^\circ - \theta) = \cos(\theta)$ can be used for angles measured in both degrees and radians.
4. Cofunction identities are derived from the sum and difference identities for trigonometric functions.
5. Understanding cofunctions helps in solving equations where angles add up to 90 degrees or $\pi/2$ radians.
Review Questions
What is the cofunction identity for $\sin(90^\circ - x)$?
If $x + y = 90^\circ$, express $\sec(x)$ in terms of a trigonometric function of $y$.
Simplify $\cot(90^\circ - \alpha)$ using a cofunction identity.
Related terms
Complementary Angles: Two angles whose measures add up to 90 degrees or $\pi/2$ radians.
Sum and Difference Identities: Formulas that express trigonometric functions of sums or differences of angles in terms of products of trigonometric functions.
Reciprocal Identities: Trigonometric identities that express each trig function as the reciprocal of another function, such as $\csc(x) = \frac{1}{\sin(x)}$.