Question 1090324
you're looking at tangent of theta = 2.798.


find the arc tangent of 2.798 and it will tell you that the angle whose tangent is 2.798 is equal to 70.3332048 degrees.


that would be the angle in the first quadrant of the unit circle.


the tangent is positive in the first quadrant and the third quadrant.


the angle in the third quadrant that is equivalent to 70.3332048 degrees in the first quadrant is equal to 180 + 70.3332048 which is equal to 250.3332048 degrees.


your two solutions are 70.3332048 degrees and 250.3332048 degrees.


if you drew a graph of the tangent function, it would look like this:


<img src = "http://theo.x10hosting.com/2017/081305.jpg" alt="$$$" </>


these angles are equivalent because the value of their tangent function is the same.


tangent of 70.3332048 degrees is equal to 2.798


tangent of 250.3332048 degrees is equal to 2.798


if you looked at the angle whose tangent is 2.798 on the unit circle, it would look like this in the first quadrant.


<img src = "http://theo.x10hosting.com/2017/081302.jpg" alt="$$$" </>


the tangent in the first quadrant is positive because the sine and the cosine are positive.


it would look like this in this in the third quadrant.


<img src = "http://theo.x10hosting.com/2017/081304.jpg" alt="$$$" </>


the reference angle is the same as the angle in the first quadrant.


it would look like this:


<img src = "http://theo.x10hosting.com/2017/081303.jpg" alt="$$$" </>


the tangent in the third quadrant is positive because the sine and the cosine are negative.


tangent = sine / cosine


positive / positive = positive (first quadrant)


negative / negative = positive (third quadrant)


here's a reference on the unit circle.


<a href = "http://www.montereyinstitute.org/courses/DevelopmentalMath/COURSE_TEXT2_RESOURCE/U19_L1_T3_text_final.html" target = "_blank">http://www.montereyinstitute.org/courses/DevelopmentalMath/COURSE_TEXT2_RESOURCE/U19_L1_T3_text_final.html</a>


if you ave any questions about this, let me know and i'll answer as best i can.