Question

an equation of the terminal side of an angle θ in standard position is given along with a restriction on x. find the indicated trigonometric function value of θ. do not use a calculator. 2x + 3y = 0, x ≥ 0; find cotθ. a. -\frac{2}{3} b. \frac{3}{2} c. \frac{13}{2} d. -\frac{3}{2}

Explanation:

Step1: Find the slope of the line

The equation of the line is \(2x + 3y=0\), rewrite it in slope - intercept form \(y=mx + b\) (where \(m\) is the slope).

$$
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$$

The slope \(m =-\frac{2}{3}=\tan\theta\) (since for the line \(y = mx\) in the context of the terminal side of an angle \(\theta\) in standard position, \(m=\tan\theta\)).

Step2: Calculate \(\cot\theta\)

We know that \(\cot\theta=\frac{1}{\tan\theta}\).
Since \(\tan\theta =-\frac{2}{3}\), then \(\cot\theta=\frac{1}{-\frac{2}{3}}=-\frac{3}{2}\)

Answer:

D. \(-\frac{3}{2}\)