Find the Exact values of the trigonometric functions of Θ from given info

Question

A few different types, for me they are extremely difficult to relate one to the other in a sense of using the same type of method to solve. I got a few correct but then started to miss some, so I got discouraged and now am asking for guidance. Thank you!

1. cot Θ = -(3/4), Θ in Q II, find cos Θ

2. sin Θ = 3/5, tan Θ < 0, find sec Θ

3. sec Θ = 3, sin Θ < 0, find cot Θ

Answer 1

Answer 2

sinθ = 3/5 and tanθ < 0.

Since sinθ > 0 and tanθ < 0, the terminal side of θ lies in Quadrant 2.

Draw ∠θ in standard position. Draw a line segment from the terminal side perpendicular to the x-axis to obtain a right triangle. The acute angle formed by the terminal side and the x-axis is the reference angle. Label the side of the triangle that is opposite the reference angle as 3 and label the hypotenuse as 5. Using the Pythagorean Theorem, the side adjacent to the reference angle has length 4.

cosθ < 0 in Quadrant 2. cosθ = - (side adjacent to the reference angle) / hypotenuse = -4/5

Do the other two problems in a similar manner.