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, a. sin 2 theta b. cos 2 theta c. tan 2 theta sin theta = 11/12 theta lies in quadrant II a tin 2 theta = (Simplify your answer Typo an exact answer, using radicals as needed Use integers or fractions for any numbers in the expression Rationalize all denominators b cos 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 tan 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

sin =opposite side/hypotenuse=11_/12

in second quadrant

opposite side = 11,hypotenuse=12

by pythogorus theorem

hypotenuse²=opposite side²+ adjacent side²

12²=11²+adjacent side²

adjacent side²=23

adjacent side=23

cos =adjacent side/hypotenuse=-(23)_/12

a)

sin2=2sincos

sin2=2*(11_/12)*(-(23)_/12)

sin2=-(1123)_/72

b)

cos2=cos²-sin²

cos2=(23_/144)-(121_/144)

cos2=-(49_/72)

c)

tan2=sin2_/cos2

tan2=(1123)_/49