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Popular >

sin(x)cos(x)=(sqrt(3))/4 ,0<= x<= 2pi

Solution

sin (x) cos (x) = \frac{3}{4}, 0 \leq x \leq 2 π

Solution

x = \frac{π}{6}, x = \frac{π}{3}, x = \frac{7 π}{6}, x = \frac{4 π}{3}

+1

Solution steps

sin (x) cos (x) = \frac{3}{4}, 0 \leq x \leq 2 π

Rewrite using trig identities

\frac{sin ( 2 x )}{2} = \frac{3}{4}

Multiply both sides by

2

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

General solutions for

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

2 x = \frac{π}{3} + 2 πn, 2 x = \frac{2 π}{3} + 2 πn

Solve

2 x = \frac{π}{3} + 2 πn : x = \frac{π}{6} + πn

Solve

2 x = \frac{2 π}{3} + 2 πn : x = \frac{π}{3} + πn

x = \frac{π}{6} + πn, x = \frac{π}{3} + πn

Solutions for the range

0 \leq x \leq 2 π

x = \frac{π}{6}, x = \frac{π}{3}, x = \frac{7 π}{6}, x = \frac{4 π}{3}

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