Suppose an angle in the 3rd quadrant has a tangent value of 0.2840. What is the measure of the angle rounded
to two decimal degrees?

To determine the angle in the third quadrant with a tangent value of 0.2840, we follow these steps:

1. First, calculate the reference angle (the positive acute angle whose tangent is 0.2840):
   \[
   \theta_{\text{ref}} = \tan^{-1}(0.2840)
   \]
   Using a calculator, the reference angle is approximately:
   \[
   \theta_{\text{ref}} \approx 15.88^\circ
   \]

2. Since the given angle is in the third quadrant, we know that the tangent is positive in this quadrant, and the angle is between \(180^\circ\) and \(270^\circ\). To find the actual angle \(\theta\), we add the reference angle to \(180^\circ\):
   \[
   \theta = 180^\circ + 15.88^\circ = 195.88^\circ
   \]

Thus, the measure of the angle is approximately **195.88°**.

Would you like more details on this calculation or have any other questions?

Here are some related questions to consider:

1. How is the tangent function defined in different quadrants?
2. Why is the tangent positive in the third quadrant?
3. How do reference angles help in finding the actual angle in trigonometry?
4. What are the signs of other trigonometric functions in the third quadrant?
5. How do you solve for angles using other trigonometric functions like sine or cosine?

**Tip:** Remember that the tangent function is positive in both the first and third quadrants.

Suppose an angle in the 3rd quadrant has a tangent value of 0.2840. What is the measure of the angle rounded to two decimal degrees?

Learn how to find the measure of an angle in the third quadrant with a tangent value of 0.2840, using trigonometric concepts and inverse functions. Follow this step-by-step guide to calculate the angle as 195.88°, suitable for high school students in Grades 10-12.

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