What is the general solution for sin(θ)cos(θ)=-1/2 ?

The general solution for sin(θ)cos(θ)=-1/2 is θ=(3pi)/4+pin

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sin(θ)cos(θ)=-1/2

sin (θ) cos (θ) = - \frac{1}{2}

θ = \frac{3 π}{4} + πn

Solution steps

sin (θ) cos (θ) = - \frac{1}{2}

Rewrite using trig identities

\frac{sin ( 2 θ )}{2} = - \frac{1}{2}

Multiply both sides by

2

sin (2 θ) = - 1

General solutions for

sin (2 θ) = - 1

2 θ = \frac{3 π}{2} + 2 πn

Solve

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

θ = \frac{3 π}{4} + πn

2 cos^{2} (x) - 3 cos (2 x) = 0

16 cos^{2} (x) = 4

3 sin (2 x - 1) - 1 = 0

cos (x) = (\frac{3}{2})

csc^{2} (θ) - 9 csc (θ) + 20 = 0

What is the general solution for sin(θ)cos(θ)=-1/2 ?
The general solution for sin(θ)cos(θ)=-1/2 is θ=(3pi)/4+pin