find all the angles exactly between 0 degrees and 360 degrees for which tan theta = -1
When finding theta for trig, remember to locate the quadrants that your trig are in. So on a graph, quadrant 1 would be positive for all trig, 2 is positive for sine, 3 is positive for tangent, and 4 is positive for cosine. Remember All Students Take Calculus acronym (ASTC). Then since you wanted to find the negative of tangent theta, that would be located in quadrants 2 and 4 since positive tangent wasn’t located in there. Now since tangent is opposite over adjacent, you need to find an angle that has sides equal in order for tan theta=1. In this case would be the 45 degree family. In 0-360 degrees the 45 degree family consists of 45, 90, 135, 180, 225, 270, 315, and 360 degrees. The only numbers that are in quadrants 2 and 4 would be 135 and 315 degrees thus that would be your answer to this question. Type it in your calculator as tan(135) and tan(315) and your answer should come up as -1.
So your answers are 135 degrees and 315 degrees.