How do you solve using CAST: sin 2θ +cos θ = 0 between 0 and 2pi?
1 Answer
Apr 27, 2018
Explanation:
#"using the "color(blue)"trigonometric identity"#
#•color(white)(x)sin2theta=2sinthetacostheta#
#rArr2sinthetacostheta+costheta=0#
#"take out "color(blue)"common factor "costheta#
#rArrcostheta(2sintheta+1)=0#
#"equate each factor to zero and solve for "theta#
#costheta=0rArrtheta=pi/2,(3pi)/2#
#2sintheta+1=0rArrsintheta=-1/2#
#"Since "sintheta<0" then "theta" is in third or fourth"#
#"quadrant"#
#theta=sin^-1(1/2)rArrtheta=pi/6larrcolor(red)"related acute angle"#
#rArrrArrtheta=(pi+pi/6)=(7pi)/6larrcolor(red)"third quadrant"#
#rArrtheta=(2pi-pi/6)=(11pi)/6larrcolor(red)"fourth quadrant"#
#rArrtheta=pi/2,(7pi)/6,(3pi)/2,(11pi)/6to(0,2pi)#