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 = - 8, sin theta

Solution

given tan=-8_/1 ,sin<0

==> cos>0

tan=opposite side/adjacent side=-8_/1

opposite side = 8, adjacent side =1

by pythogorus theorem

hypotenuse²=opposite side²+ adjacent side²

hypotenuse²=8²+1²

hypotenuse²=65

hypotenuse=65

sin =opposite side/hypotenuse= -8_/65

cos =adjacent side/hypotenuse= 1_/65

a)sin(2) =2sincos

sin(2)=2(-8_/65)(1_/65)

sin(2)=(-16_/65)

b)cos(2)=cos²-sin²

cos(2)=(1_/65)²-(-8_/65)²

cos(2)=(1_/65)-(64_/65)

cos(2)=-(63_/65)

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

sin(_/2) =[(1-(1_/65))_/2]

sin(_/2) =[(65- 1)_/265]

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

cos(_/2) =-[(1+(1_/65))_/2]

cos(_/2) =-[(65+ 1)_/265]