Question 752005
find the exact value of cos 2A and sin 2A given sin A = 12/13, A is in quadrant I

{{{sin(A)=12/13}}}
{{{cos(A)=5/13}}} ( working with 5-12-13 right triangle)

{{{sin(2A)=2sin(A)cos(A)=2*12/13*5/13=120/169}}}
..
{{{cos(2A)=cos^2(A)-sin^2(A)=25/169-144/169=-119/169}}}
..
Check with calculator:
sin(A)=12/13 (in Q1)
A=67.38º
2A=134.76
sin(2A)=sin(134.76º)≈0.71
exact value=120/169≈0.71
cos(2A)=cos(134.76º)≈-0.704
exact value=119/169≈-0.704