How do you find the exact value of #costheta=3sin2theta# in the interval #0<=theta<2pi#?

Question

2630 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-07-24T06:24:12

The solutions are #S={pi/2, 3/2pi, 0.167, 2.974}#

The equation is

#costheta=3sin2theta#

But

#sin2theta=2sinthetacostheta#

Therefore,

#costheta=6sinthetacostheta#

#costheta-6sinthetacostheta=0#

#costheta(1-6sintheta)=0#

#=>#, #{(costheta=0),(1-6sintheta=0):}#

#=>#, #{(costheta=0),(sintheta=1/6):}#

#costheta=0#, #=>0#, #{(theta=pi/2),(theta=3/2pi):}#

#sintheta=1/6#, #=>#, #{(theta=0.167),(theta=2.974):}#

The solutions are #S={pi/2, 3/2pi, 0.167, 2.974}#