How do you solve this? Solve the equation for exact solutions in the interval [0degrees,360degrees). Use an algebraic method.

Question

(cot #theta#-1)(2sin+1)=0

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Answer 1 · 2018-05-07T07:42:21

#thetain{45^@,225^@,210^@,330^@}#

As #(cottheta-1)(2sintheta+1)=0#

we have either #cottheta-1=0# i.e. #cottheta=1=cot45^@#

and #theta={45^@,225^@}# in the interval #[0^@,360^@]#

or #2sintheta+1=0# i.e. #sintheta=-1/2=-sin30^@#

and #theta={210^@,330^@}# in the interval #[0^@,360^@]#