Use the information given about the angle theta 0 lessthanor

Use the information given about the angle theta, 0 lessthanorequalto theta lessthanorequalto 2 pi, to find the exact value of each trigonometric function tan theta = -6, sin theta

Solution

given tan=-6_/1 ,sin<0

==> cos>0

tan=opposite side/adjacent side=-6_/1

opposite side = 6, adjacent side =1

by pythogorus theorem

hypotenuse²=opposite side²+ adjacent side²

hypotenuse²=6²+1²

hypotenuse²=37

hypotenuse=37

sin =opposite side/hypotenuse= -6_/37

cos =adjacent side/hypotenuse= 1_/37

a)sin(2) =2sincos

sin(2)=2(-6_/37)(1_/37)

sin(2)=(-12_/37)

b)cos(2)=cos²-sin²

cos(2)=(1_/37)²-(-6_/37)²

cos(2)=(1_/37)-(36_/37)

cos(2)=-(35_/37)

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

sin(_/2) =[(1-(1_/37))_/2]

sin(_/2) =[(37- 1)_/237]

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

cos(_/2) =-[(1+(1_/37))_/2]

cos(_/2) =-[(37+ 1)_/237]