Given that sin 58 and cos0 do not rationalize the denominato

Given that sin= 5/8 and cos<0,

a) find tan and sec

b) find the exact value of sin (cos^-1 3/4)

c) write the given expression as an algebraic expression: cos (sin^-1 x/ sqrt(25 + x²) for x>0 do not rationalize the denominator

Solution

sin= 5/8 and cos<0

cos= -[8²-5²] /8

cos= -(39)/8

a)tan=sin/cos =(5/8)/(-(39)/8)

tan=sin/cos =-5/39

sec=1/cos =1/(-(39)/8) =-8/39

b) sin (cos^-1 3/4)

sin (sin^-1 ((4²-3²))/4)

sin (sin^-1 (7)/4)

=(7)/4

c)cos (sin^-1 x/ sqrt(25 + x²))

cos (cos^-1 5/ sqrt(25 + x²))

=5/sqrt(25 + x²)