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?

Given that the tangent of an angle in the 3rd quadrant is \( \tan(\theta) = 0.2840 \), we can calculate the angle as follows:

1. Find the reference angle using the arctangent function:
   \[
   \theta_{ref} = \tan^{-1}(0.2840)
   \]
   The reference angle is the angle in the 1st quadrant with the same tangent value.

2. Since the given angle is in the 3rd quadrant, the actual angle is found by adding \(180^\circ\) to the reference angle.

Now let's calculate:

\[
\theta_{ref} = \tan^{-1}(0.2840) \approx 15.88^\circ
\]

3. Therefore, the angle in the 3rd quadrant is:
\[
\theta = 180^\circ + 15.88^\circ = 195.88^\circ
\]

Thus, the angle is approximately \( \boxed{195.88^\circ} \).

Would you like more details on any of these steps, or do you have any other questions?

Here are 5 related questions:
1. What are the characteristics of angles in different quadrants?
2. How do you find the reference angle for any trigonometric function?
3. How does the sign of the tangent function vary across quadrants?
4. Can you explain the inverse trigonometric functions and their use?
5. How do you calculate angles for trigonometric functions in the 2nd or 4th quadrants?

**Tip:** Always remember the sign of trigonometric functions changes depending on the quadrant.

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 3rd quadrant with a given tangent value of 0.2840. This trigonometry problem involves calculating the reference angle using the arctangent function and applying the appropriate adjustment for the 3rd quadrant. Suitable for high school students in Grades 9-12.

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