What is the general solution for 3+1/5 cos(θ/3+(7pi)/4)=3 ?

The general solution for 3+1/5 cos(θ/3+(7pi)/4)=3 is θ=6pin-(15pi)/4 ,θ=6pin-(3pi)/4

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3+1/5 cos(θ/3+(7pi)/4)=3

3 + \frac{1}{5} cos (\frac{θ}{3} + \frac{7 π}{4}) = 3

θ = 6 πn - \frac{15 π}{4}, θ = 6 πn - \frac{3 π}{4}

Solution steps

3 + \frac{1}{5} cos (\frac{θ}{3} + \frac{7 π}{4}) = 3

Subtract

3

from both sides

3 + \frac{1}{5} cos (\frac{θ}{3} + \frac{7 π}{4}) - 3 = 3 - 3

Simplify

\frac{1}{5} cos (\frac{θ}{3} + \frac{7 π}{4}) = 0

Multiply both sides by

5

cos (\frac{θ}{3} + \frac{7 π}{4}) = 0

General solutions for

cos (\frac{θ}{3} + \frac{7 π}{4}) = 0

\frac{θ}{3} + \frac{7 π}{4} = \frac{π}{2} + 2 πn, \frac{θ}{3} + \frac{7 π}{4} = \frac{3 π}{2} + 2 πn

Solve

\frac{θ}{3} + \frac{7 π}{4} = \frac{π}{2} + 2 πn : θ = 6 πn - \frac{15 π}{4}

Solve

\frac{θ}{3} + \frac{7 π}{4} = \frac{3 π}{2} + 2 πn : θ = 6 πn - \frac{3 π}{4}

θ = 6 πn - \frac{15 π}{4}, θ = 6 πn - \frac{3 π}{4}

sin (θ) = - \frac{13}{7}

- 2 sin (x) = - 2

sin (π - x) = cos (\frac{3 π}{2} - x) + cos (π)

4 csc (x) + 8 = 0

2 cos (2 θ) + 3 = 2

What is the general solution for 3+1/5 cos(θ/3+(7pi)/4)=3 ?
The general solution for 3+1/5 cos(θ/3+(7pi)/4)=3 is θ=6pin-(15pi)/4 ,θ=6pin-(3pi)/4