Math Problem Statement

The angle [\theta_1] is located in Quadrant [\text{II}], and

[\sin(\theta_1)=\dfrac{9}{41}] . What is the value of [\cos(\theta_1)]? Express your answer exactly. [\cos(\theta_1)=]

Solution

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Math Problem Analysis

Mathematical Concepts

Trigonometry
Quadrants
Pythagorean Identity

Formulas

\(\sin^2(\theta) + \cos^2(\theta) = 1\)
Pythagorean identity for sine and cosine

Theorems

Pythagorean Theorem
Sign rules in Quadrants

Suitable Grade Level

Grades 9-12