if tan t = 3/4 and pi<t<(3*pi)/(2), find sin t, cos t, sec t, csc t, cot t. enter the exact answers

Answer 1

tant = 3/4 = 0.75 in quadrant III

cott = 4/3 = 1 1/3

sint = -3/5 = -.0.6

csct = -5/3 = -1 2/3

cost = -4/5 = -.0.8

sect = -5/4 = -1.25

all trig functions in quadrant 3 are negative except tangents and cotangents

hypotenuse = square root of (opposite side squared + adjacent side squared) = sqr((-3)^2 +(-4)^2)= sqr(9+16) = 25= 5

hypotenuse = 5

opposite side = -3

adjacent side = -4

tant = opposite over adjacent

cott = adjacent over opposite

sint = opposite over hypotenuse

csct = hypotnuse over opposite

cost = adjacent over hypotenuse

sect = hypotenuse over adjacent