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

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

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sin(x)*cos(x)= 1/4

sin (x) \cdot cos (x) = \frac{1}{4}

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

Solution steps

sin (x) cos (x) = \frac{1}{4}

Rewrite using trig identities

\frac{sin ( 2 x )}{2} = \frac{1}{4}

Multiply both sides by

2

sin (2 x) = \frac{1}{2}

General solutions for

sin (2 x) = \frac{1}{2}

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

Solve

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

Solve

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

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

sin (θ) = \frac{- 3}{2}, 0 \leq θ \leq 4 π

4 sin (θ) + 4 = \frac{- 3}{sin ( θ ) - 1}

cos (θ) = 0.707

\frac{1}{( 1 + tan ^{2} ( o ) + 1 )} + \frac{1}{( 1 + cot ^{2} ( o ) )} = 1

9 (2 sin^{2} (x) - 1) = 0

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