Cofunction Identities Examples & Practice Problems Trigonometry

TL;DR

Cofunction identities state that sine is equal to cosine, tangent is equal to cotangent, and secant is equal to cosecant, when two angles add up to 90 degrees.

Transcript

in this video i'm going to focus on cofunction identities so here are some formulas that you need to know sine theta is equal to cosine 90 minus theta and cosine theta is equivalent to sine 90 minus theta tangent is equal to the cofunction cotangent 90 minus theta and so cotangent is also equal to tangent 90 minus theta secant is equal to cosecant ... Read More

Key Insights

• 💨 Cofunction identities provide a way to simplify and find equivalent values for trigonometric functions.
• 👨‍💼 The relationships between sine and cosine, tangent and cotangent, and secant and cosecant can be understood through cofunction identities.
• 🔺 Cofunction identities can be applied to angles given in degrees or radians, using the appropriate conversion.
• ❓ Using cofunction identities can make solving trigonometric equations and problems more efficient.
• ❓ Understanding how to apply cofunction identities is a fundamental skill in trigonometry.
• 🙃 Cofunction identities are derived from the relationship between the sides of a right triangle.
• 🔺 Cofunction identities can be used to find the value of an unknown angle given its cofunction.

Questions & Answers

Q: What is a cofunction identity?

A cofunction identity is a relationship between trigonometric functions, stating that two specific functions are equal when the sum of the angles involved is 90 degrees. For example, sine is equal to cosine.

Q: How are cofunction identities used in practice?

Cofunction identities can be applied to find equivalent values of trigonometric functions. By finding the cofunction of a given angle, the equation can be simplified and solved more easily.

Q: What is the cofunction of tangent?

The cofunction of tangent is cotangent. This means that when given an angle in tangent, the equivalent cofunction value can be found by subtracting the angle from 90 degrees.

Q: Can cofunction identities be used with angles in radians?

Yes, cofunction identities can be used with angles in radians. Instead of subtracting from 90 degrees, the given angle should be subtracted from pi/2 (90 degrees in radians) to find the equivalent cofunction value in radians.

Summary & Key Takeaways

• Cofunction identities state that sine is equal to cosine, tangent is equal to cotangent, and secant is equal to cosecant.

• By using 90 minus the given angle, the cofunction identities can be applied to find the equivalent value.

• Examples are given to demonstrate how to apply cofunction identities in various scenarios.