1 Simplifysectcostsint to a single trig function 2 If sin

1. Simplify((sec(t)-cos(t)))/(sin(t)) to a single trig function.

2. If sin ( ) = 4/5 sin()=-45, and is in quadrant IV , then find (a) cos() (b) tan() (c) sec() (d) csc() (e) cot()

3. If =1/6 then find exact values for the following: (a) sec() (b)csc() (c)tan() (d)cot()

1) (sec(t)-cos(t)))/(sin(t)) = [(1/cos t) - cos t]/sin t = (1 - cos^2 t)/cos t*sin t = sin^2 t/(cos t* sin t) = tan t

2) sin()=-4/5

cos = sqrt[1 - sin^2 ] = sqrt[1 - 16/25] = 3/5

tan = (-4/5)/(3/5) = -4/3

sec = 1/cos = 5/3

csc = 1/sin = -5/4

cot = 1/tan = -3/4

3) = /6

sec(/6) = 2/sqrt(3)

csc(/6) = 2

tan(/6) = 1/sqrt(3)

cot(/6) = 1/tan(/6) = sqrt(3)