How do you solve -6 cos (pi/3) theta = 4?

1 Answer
Ratnaker Mehta
Jun 13, 2016

:. theta=3(2k+1)-(3/pi)arccos(2/3), k in ZZ.

Explanation:

Eqn. costheta=cosalpha has solution set {(2kpi+alpha): kin ZZ}

The given eqn. is -6cos(pi/3)theta=4.
:.cos(pi/3)theta= -4/6 = -2/3 = cos(pi - arccos(2/3))= cosalpha, where alpha=pi-arccos(2/3).
;. (pi/3)theta=2kpi+alpha= 2kpi+pi-arccos(2/3)= (2k+1)pi-arccos(2/3), k inZZ.
:. theta=(3/pi){(2k+1)pi-arccos(2/3)] = 3(2k+1)-(3/pi)arccos(2/3), k in ZZ.

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