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

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

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Answer 1 · 2016-06-13T18:26:33

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

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