Point Q ( -4, -5) lies on the terminal arm of an angle θ in standard position

Question

(a) sketch a diagram, showing all the important information.

 (b) determine the three reciprocal trigonometric ratios of angle θ in exact form.

(c) find angle θ to the nearest degree.

Answer 1

a) https://ibb.co/vVmpJXt

b) Since tanθ = perpendicular/ base = 5/4

And hypotenuse = √(5^2 + 4^2) = √41

So, cotθ = base/perpendicular = 4/5

secθ = hypotenuse/ base = √41/4

And cosecθ = hypotenuse/ perpendicular = √41/5

c) θ = arctan(5/4)

or θ = 51.34 degrees