https://file.aiquickdraw.com/mathbot/file/1726088104109boq8ryfu.jpg

The problem asks you to use the reciprocal identities to solve for \( \cot \theta \) when \( \tan \theta = a \) (with \( a \neq 0 \)).

We know the reciprocal identity between tangent and cotangent is:
\[
\cot \theta = \frac{1}{\tan \theta}
\]

Given that \( \tan \theta = a \), we substitute this into the equation:
\[
\cot \theta = \frac{1}{a}
\]

Thus, the solution is:
\[
\cot \theta = \frac{1}{a}
\]

Would you like further details or have any questions? Here are five related questions you might find helpful:

1. What are the reciprocal identities for sine, cosine, and tangent?
2. How do you derive the reciprocal identity for cotangent from the definition of tangent?
3. Can you express \( \cot \theta \) in terms of sine and cosine?
4. How do you solve for \( \theta \) if both \( \tan \theta \) and \( \cot \theta \) are given?
5. What happens to \( \cot \theta \) when \( \tan \theta \) approaches zero?

**Tip**: Always remember that reciprocal identities are useful for simplifying trigonometric expressions.

Learn how to find cot(θ) using reciprocal identities when tan(θ) = a (a ≠ 0). This problem explores key trigonometric concepts and reciprocal identities. Suitable for high school students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation