What is the general solution for sin(θ)cos(θ)= 1/4 ?

The general solution for sin(θ)cos(θ)= 1/4 is θ= pi/(12)+pin,θ=(5pi)/(12)+pin

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sin(θ)cos(θ)= 1/4

sin (θ) cos (θ) = \frac{1}{4}

θ = \frac{π}{12} + πn, θ = \frac{5 π}{12} + πn

Solution steps

sin (θ) cos (θ) = \frac{1}{4}

Rewrite using trig identities

\frac{sin ( 2 θ )}{2} = \frac{1}{4}

Multiply both sides by

2

sin (2 θ) = \frac{1}{2}

General solutions for

sin (2 θ) = \frac{1}{2}

2 θ = \frac{π}{6} + 2 πn, 2 θ = \frac{5 π}{6} + 2 πn

Solve

2 θ = \frac{π}{6} + 2 πn : θ = \frac{π}{12} + πn

Solve

2 θ = \frac{5 π}{6} + 2 πn : θ = \frac{5 π}{12} + πn

θ = \frac{π}{12} + πn, θ = \frac{5 π}{12} + πn

cos^{2} (x) + 13 cos (x) = 14

3 tan (θ) = 33

sin (x) = - \frac{5}{3}

tan (a) = 2.4

cos (x) - sin (x) = 1, 0 \leq x \leq 2 π

What is the general solution for sin(θ)cos(θ)= 1/4 ?
The general solution for sin(θ)cos(θ)= 1/4 is θ= pi/(12)+pin,θ=(5pi)/(12)+pin