# Chapter 1 - Trigonometric Functions - Section 1.4 Using the Definitions of the Trigonometric Functions - 1.4 Exercises: 66

$\cot\theta=\sqrt 3$

#### Work Step by Step

1.We get this information from the given cosecant value $y=-1$ $r=2$ 2. We can use y and r to find x (we need to remember that sign of x depends on quadrant, since it ends in quadrant III, x must be negative) $r=\sqrt {y^{2}+x^{2}}$ $x=-\sqrt {r^{2}-y^{2}}=-\sqrt {(2)^{2}-(-1)^{2}}=-\sqrt {3}$ 4. Then insert values, $\cot\theta=\sqrt 3$

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