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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

sin(x)cos(x)= 1/2

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

x = \frac{π}{4} + πn

Solution steps

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

Rewrite using trig identities

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

Multiply both sides by

2

sin (2 x) = 1

General solutions for

sin (2 x) = 1

2 x = \frac{π}{2} + 2 πn

Solve

2 x = \frac{π}{2} + 2 πn : x = \frac{π}{4} + πn

x = \frac{π}{4} + πn

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

12 sin^{2} (x) - 13 sin (x) + 3 = 0

sin (θ) = \frac{1}{2}

csc^{2} (x) - 1 = 0

csc (θ) = \frac{2 3}{3}

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