Question

if sin o= 1/2....what are the exact ratios for the other five trig ratios?

Answer 1

remember that

sin^2 + cos^2 = 1

so

sin^2 + cos^2 = 1

(1/2)^2 + cos^2 = 1

1/4 + cos^2 = 1

cos^2 = 1 - 1/4

cos^2 = 3/4

cos = sqrt(3/4) ... see note below

cos = sqrt(3)/2


Note: the sign of the square root will depend on where the angle theta is. If theta is in quadrants 1 or 4, then cosine is positive here. If theta is in quadrants 2 or 3, then cosine is negative here

Answer 2

once you know sine and cosine, you can find tangent since

tan = sin/cos

Answer 3

then you would use these 3 to find csc, sec, and cot