If sec t =5/4, and t is in quadrant IV, find sin t, cos (-t), cot t, csc t, and [tan t] , [cot (-t)]

Question

I am confused little bit about signs if sin t is negetive or positive and not sure if my answers are correct. Please help!

Answer 1

sec=5/4=1/cosα

1.25= " "

1.25*cosα=1

1/1.25=cosα

.8=cosα

α=36.869...°

4thquad=α=216.869....°

sinα=-.599....

α=t

Answer 2

Draw a picture to start. That always helps. If secant is 5/4 then hypotenuse h=5 and adjacent a=4

Then the third side opposite o=3 by pythagorean’s theorem

Sin t=-3/5as sin is negative in quadrant 4

cos t = 4/5 and cos(-t) is the same as cos(t) it sound be in quadrant 1

cot(t) =a/o=-4/3 Tangent and Cotangent are both negative in quadrant 4

csc(t)is h/o or 1/sin=-5/3

tan(t) is o/a or -3/4

cot-t) would be in quadrant 1 so it and tangent will both be positive It is 4/3