Find the values of the trigonometric functions of t from the

Find the values of the trigonometric functions of t from the given information.

sin(t) =

, sec(t) < 0

Solution

given

sin t = -1/4 opposite side = 1, hypotenuse = 4

adj. side = (4^2 - 1) = 15

since sec and sin are negative, t is in III quadrant, where only tan and cot are positive.

sin t = -1/4, csc t = -4 since cscx=1/sinx

cos^(2)t=1-sin^2(t)=1-1/16=15/16

cos t = -15 / 4, sec t = -4 /15 since secx=1/cosx

since tanx=sinx/cosx

tan t = 1/15, cot t = 15 cotx=1/tanx