What is the general solution for 6sin(θ/2)=-6cos(θ/2) ?

The general solution for 6sin(θ/2)=-6cos(θ/2) is θ=(3pi)/2+2pin

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6sin(θ/2)=-6cos(θ/2)

6 sin (\frac{θ}{2}) = - 6 cos (\frac{θ}{2})

θ = \frac{3 π}{2} + 2 πn

Solution steps

6 sin (\frac{θ}{2}) = - 6 cos (\frac{θ}{2})

Rewrite using trig identities

6 tan (\frac{θ}{2}) = - 6

Divide both sides by

6

tan (\frac{θ}{2}) = - 1

General solutions for

tan (\frac{θ}{2}) = - 1

\frac{θ}{2} = \frac{3 π}{4} + πn

Solve

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

θ = \frac{3 π}{2} + 2 πn

csc (θ) = - \frac{4}{3}

9 sin^{2} (θ) + 3 cos (θ) - 9 = - 2

2 cos (3 t) - 1 = 0

sin (x) + cos (x) - 1 = 0

tan (θ) = - 9

What is the general solution for 6sin(θ/2)=-6cos(θ/2) ?
The general solution for 6sin(θ/2)=-6cos(θ/2) is θ=(3pi)/2+2pin