Question

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

Answer 1

`:. 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.`