Suppose that tan0=3/5 and that π<0< 3π/2 . Find the values of sinθ, cos0, csc0, sec0, and cot0.

Question

sinθ=?

cosθ=?

cscθ=?

secθ=?

cotθ=?

Answer 1

tanx = 3/5 = opposite side over adjacent side. Hypotenuse = sqr(5^2 + 3^2) = sqr34

x is in quadrant I or III, where tangents >0

cotx 1/tanx = 5/3

sinx = -3/sqr34 = about -3/5.8 = -.52 in quadrant III, but sinx = 3/sqr34 = about 0.52 in quadrant I

cscx =-sqr34/3 or sqr34/3 = about + or - 5.8/3 = +1.9

cosx =-5/sqr34 or 5/sqr34 = about + or - 5/5.8 = +0.86

secx=- sqr34/5 or sqr34/5 = about + or - 5.8/5 = + 1.16

x = about 31 degrees

or in quadrant III, x = about 211 degrees