Trigonometry Triangles

Question

Hello I currently need help with the following trigonometry question. I believe I need to draw a diagram of a traingle from the information given and then begin solving but I am not sure.

If tan t =−3/4 and π/2 < t< π, find sin t, cos t, sec t, csc t, cot t.

Answer 1

You have the idea. Since t is between 90 and 180, the angle is in quadrant II, where all x coordinates are negative and all y coordinates are positive. The Pythagorean theorem tells you that the hypotenuse will be 5 with the horizontal leg as -4 and vertical leg as 3, i.e. the tangent is -3/4. Also you might recognize this as a 3-4-5 right triangle without having to use the Pythagorean Theorem. Now you can deduce the other 5 trig ratios. For example, sin t = 3/5 (opposite/hypotenuse).