If sin x = 1 4 sinx=14 , x in quadrant I, then find (without finding x) precalculus

Question

If sin x = 1/4 , x in quadrant I, then find (without finding x)

sin(2x)=

cos ( 2 x ) =

tan ( 2 x ) =

Answer 1

cos2x = 1 - 2sin²x = 1 - 2(1/4)² = 7/8 > 0. So, 2x still in quadrant I

tan2x = √1/cos²2x - 1 = √(64/49 - 1) = √15/7;

sin2x = tan2x·cos2x = √15/7·7/8 = √15/8

Answer 2

If sin x = 1/4 in QI, cos x = ? (Use Pythagoras)

Now substitute into appropriate formula.