Problem

Determine the values of $\theta$, where $0 \leq \theta \leq 360$, such that $\tan \theta=-\frac{1}{\sqrt{3}}$. Place numerical value only of theta in the two blanks with the smaller one first.

Solution

Step 1 :The tangent function has a period of 180 degrees. This means that if \(\tan \theta = -\frac{1}{\sqrt{3}}\), then \(\tan (\theta + 180) = -\frac{1}{\sqrt{3}}\) as well.

Step 2 :We know that \(\tan 30 = \frac{1}{\sqrt{3}}\) and \(\tan 150 = -\frac{1}{\sqrt{3}}\).

Step 3 :Therefore, the solutions to the equation \(\tan \theta = -\frac{1}{\sqrt{3}}\) in the interval \(0 \leq \theta \leq 360\) are \(\theta = 150\) and \(\theta = 150 + 180 = 330\).

Step 4 :Final Answer: The values of \(\theta\) that satisfy the equation \(\tan \theta = -\frac{1}{\sqrt{3}}\) in the interval \(0 \leq \theta \leq 360\) are \(\boxed{150}\) and \(\boxed{330}\).

From Solvely APP
Source: https://solvelyapp.com/problems/33038/

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