If sin x = 2/5, x in quadrant I, then find (without finding x)

Question

If sin x = 2/5 sinx=25 , x in quadrant I, then find (without finding x)

sin ( 2 x ) =

cos(2x)=

tan(2x)=

Please explain clear it takes time for me to understand

Answer 1

sinx = 2/5 = opposite side over hypotenuse = o/h o=2, h= 5

cosx = adjacent side over hypotenuse = a/h. a= sqr(h^2 -o^2 = sqr(5^2 -2^2) = sqr(25-4) = sqr21

cosx = sqr21/5

double angle formulas are

sin2x = 2sinxcosx = 2(2/5)(sqr21/5) = 4sqr21/25

sin2x = (4sqr21)/25

cos2x = (sqr21/5)^2 - (2/5)^2 = 21/25 - 4/25 = (21-4)/25 = 17/25

cos2x = 17/25

tan2x = sin2x/cos2x = (4sqr21/25)/(17/25) = 4sqr21/25

tan2x = (4sqr21)/25

Answer 2

Check it out!