Trigonometry Graphing

Question

Suppose that sect= -4/3 and that cott > 0. What is the value of csct?

Answer 1

sect is 1/cost. cost = adjacent side divided by hypotenuse

sect = hypotenuse divided by the adjacent side = 4/-3

hypotenuse is always >0. -3<0 which means t is in the 2nd or 3rd quadrants. cott>0 means 1st or 3rd quadrant. that narrows t down to the 3rd quadrant.

csct = 1/sint sint<0 in the 3rd quadrant, and csct<0

opposite side = -square root of 16-9 = -sqr7

csct = hypotenuse over opposite side = 4/-sqr7 = -4/sqr7 = (-4/7)sqr7 = about -1.51

reference angle is cos^-1(3/4) = 41.41 degrees

sin41.41 = .66

csc41.41 = 1/sin41.41 = 1/.66 = about 1.51

since t is in the 3rd quadrant

add 180 to 41.41= 221.41

csc221.41= about -1.51