Question

Given that cos(theta)= -3/5 and theta is in quadrant III, find the exact value of tan2(theta)

Please show an explanation

Answer 1

If we look up the arc cosine of -3 / 5 (or -.6) it equals 126.87 degrees.
But this angle is in Quadrant II.
All arc functions have 2 angles between 0 and 360.
To find the second arc cosine angle, we subtract 126.87 from 360 degrees.
360 -126.87 = 233.13
233.13 lies in sector III and the arc cosine of 233.13 equals -.6.

Answer 2

By the Pythagorean theorem, the missing side measures -4 (cuz it's in the 3rd quadrant where y is negative). So the tangent then would be 4/3, and squaring that would give you 16/9