Questions: cot θ = -√3 Find two angles between 0 degrees and 360 degrees

Solution Steps

To find the angles where \(\cot \theta = -\sqrt{3}\), we need to determine the angles where the cotangent function has this value. Since \(\cot \theta = \frac{1}{\tan \theta}\), we can find the corresponding tangent value and then determine the angles in the specified range.

Given that \( \cot \theta = -\sqrt{3} \), we can find the corresponding tangent value using the relationship \( \tan \theta = \frac{1}{\cot \theta} \). Thus, we have: \[ \tan \theta = \frac{1}{-\sqrt{3}} = -\frac{1}{\sqrt{3}} \approx -0.5774 \]

To find the reference angle, we calculate: \[ \theta_{\text{ref}} = \tan^{-1}(-\frac{1}{\sqrt{3}}) \] This gives us a reference angle of: \[ \theta_{\text{ref}} \approx -30^\circ \] However, we need the positive equivalent, which is \( 30^\circ \).

Since \( \tan \theta \) is negative, the angles will be located in the second and fourth quadrants. Therefore, we calculate: \[ \theta_1 = 180^\circ - 30^\circ = 150^\circ \] \[ \theta_2 = 360^\circ - 30^\circ = 330^\circ \]

Final Answer