triganometry question

Question

suppose that sinx=5/13 and x is between 0degrees and 90degrees. answer each question in rational, radical form.

a.find cos x

b.find sin (2x)

c.find cos(x/2)

Answer 1

sinx=5/13 = opposite side over hypotenuse

adjacent side = square root of 13^2 - 5^2 = sqr(169-25) = sqr(144) = 12

cosx = adjacent side/hypotenuse = 12/13

sin2x = 2sinxcosx = 2(5/13)(12/13) = 120/169

cos(x/2) = sqr((1+cosx)/2) = sqr((1+12/13)/2) = sqr 25/26 = 5sqr(1/26)

cosx =12/13 means x is a very small angle. cos(0) = 1, so cos(a small angle) is close to 1

cut that small angle in half, and you're even closer to 1 for the cosine. 5sqr(1/26) is closer to 1 than 12/13