# Chapter 1 - Trigonometric Functions - Section 1.4 Using the Definitions of the Trigonometric Functions - 1.4 Exercises: 67

$\cot\theta=3.447019$

#### Work Step by Step

1. We will use the identity $1+\cot^{2}\theta=\csc^{2}\theta$ 2. Substitute the values $1+\cot^{2}\theta=(-3.5891420)^{2}$ $\cot^{2}\theta=12.8819403-1$ $\cot^{2}\theta=11.8819403$ $\cot\theta=+-3.447019$ 3. To figure out the sign we need to pay attention to the quadrant, here, Q3, cotangent is positive. $\cot\theta=3.447019$

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