If sin x=2/9,x, in quadrant i, then find(without findingx): sin(2x), cos(2x), tan(2x)

We have that
sin x=2/9

we know that
sin² x+cos² x=1> cos² x=1-sin² x> cos² x=1-(2/9)²
cos² x=1-(4/81)> (81-4)/81> 77/81
cos x=√(77/81)

Sin 2x = 2 sin x cos x> 2*(2/9)*(√(77/81))> (4/81)*√77---> 0.43

Sin 2x=0.43
so
cos² 2x=1-sin² 2x> 1-[0.43]²> 1-[0.1878]> 0.81
cos² 2x=0.81> cos 2x=0.9

tan 2x=sin 2x/cos 2x> tan 2x=0.43/0.9> tan 2x=0.48

the answers are
sin 2x=0.43
cos 2x=0.9
tan 2x=0.48

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