How do you find the solution to #6cos^2theta+5costheta-4=0# if #0<=theta<360#?

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Answer 1 · 2018-05-25T06:02:54

The solutions are #S={60^@, 300^@}# for #theta in [0, 360)#

This is a quadratic equation in #costheta#

#6cos^2theta+5costheta-4=0#

The discriminant is

#Delta=b^2-4ac=5^2-4(6)(-4)=121#

As #Delta >0#, there are #2# real solutions

#{(costheta_1=(-5+sqrt121)/(12)=(-5+11)/12),(costheta_2=(-5-sqrt121)/(12)=(-5-11)/12):}#

#{(costheta_1=6/12=1/2),(costheta_2=-1.33):}#

#{(theta_1=60^@ ;300^@),(theta_2=O/):}#

The solutions are #S={60^@, 300^@}# for #theta in [0, 360)#