Use the given information to find the exact value of each of

Use the given information to find the exact value of each of the following, sin 2 theta cos 2 theta tan 2 theta sin theta = 3/8, theta lies in quadrant II sin 2 theta = (Simplify your answer. Type an exact answer, using radicals as needed. Use integers or fractions for any numbers in the expression. Rationalize all denominators.)

Solution

given in second quadrant

90<<180

=>180<2<360

given sin =3/8

cos=(-(8²-3²))/8

cos=(-55)/8

sin2 =2sin cos =2(3/8)((-55)/8) =(-655)/64=(-355)/32

cos2=cos²-sin²=(55/64)-(9/64)=46/64=23/32

tan2=sin2/cos2 =((-355)/32)/(23/32)=(-355)/23