sec v = 13/5, 3 pie/2 < v < 2 pie

Question

Find the exact value of the trigonometric function given that tan u = -3/4, pie/2 < u < pie

Answer 1

Given sec v = 13/5 = hypotenuse / adjacent,  and it located in IV quadrant given 3 π/2 < v < 2 π

Then, hypotenuse = 13, adjacent = 5, and opposite = -12

Therefore,

sin v = opposite / hypotenuse = -12/13

cos v = adjacent / hypotenuse = 5/13

tan v = opposite / adjacent = -12/5 

cot v = adjacent / opposite = 5/-12 = -5/12

cosec v = hypotenuse / opposite = 13/-12 = -13/12

 

Given tan u = -3/4 = 3/-4= opposite / adjacent, and it located in II quadrant given π/2 < u < π

Then, hypotenuse = √(3² + 4²) = 5, adjacent = -4, opposite = 3

Therefore,
sin u = opposite / hypotenuse = 3/5
cos u = adjacent / hypotenuse = -4/5
cot u = adjacent / opposite = -4/3

sec u = hypotenuse / adjacent = 5/-4 = -5/4
cosec u = hypotenuse / opposite = 5/3