If tan theta 78 pi Solutiontanopposite sideadjacent side78

Solution

tan=opposite side_{/adjacent side}=7_/8 ,<<3_/2

hypotenuse²=opposite side²+ adjacent side²

hypotenuse²=7²+ 8²

hypotenuse=113

sin =opposite side/hypotenuse= -7_/113

cos =adjacent side/hypotenuse= -8_/113

a)

sin(2)=2sincos

sin(2)=2(-7_/113)(-8_/113)

sin(2)=112_/113

b)

cos(2)=1-2sin²

cos(2)=1-2(-7_/113)²

cos(2)=1-(98_/113)

cos(2)=(15_/113)

c)sin(_/2)=[(1-cos)_/2]

sin(_/2)=[(1-(-8_/113))_/2]

sin(_/2)=[(113 +8)_/2113]

d)cos(_/2)=-[(1+cos)_/2]

cos(_/2)=-[(1+(-8_/113))_/2]

cos(_/2)=-[(113 -8)_/2113]