What is the general solution for 36sin(x)cos(x)=-9sqrt(3) ?

The general solution for 36sin(x)cos(x)=-9sqrt(3) is x=(2pi)/3+pin,x=(5pi)/6+pin

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

36sin(x)cos(x)=-9sqrt(3)

36 sin (x) cos (x) = - 93

x = \frac{2 π}{3} + πn, x = \frac{5 π}{6} + πn

Solution steps

36 sin (x) cos (x) = - 93

Rewrite using trig identities

36 \cdot \frac{sin ( 2 x )}{2} = - 93

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

\frac{sin ( 2 x ) \cdot 36}{2} = - 93

Divide the numbers:

\frac{36}{2} = 18

18 sin (2 x) = - 93

Divide both sides by

18

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

General solutions for

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

2 x = \frac{4 π}{3} + 2 πn, 2 x = \frac{5 π}{3} + 2 πn

Solve

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

Solve

2 x = \frac{5 π}{3} + 2 πn : x = \frac{5 π}{6} + πn

x = \frac{2 π}{3} + πn, x = \frac{5 π}{6} + πn

sin (2 x) = cos (4 x)

6 cos^{2} (θ) + 7 = - 17 cos (θ)

0 = - 9 \cdot sin (2 x)

sec^{2} (x) = 4 tan^{2} (x)

5 sin (x) = - 4

What is the general solution for 36sin(x)cos(x)=-9sqrt(3) ?
The general solution for 36sin(x)cos(x)=-9sqrt(3) is x=(2pi)/3+pin,x=(5pi)/6+pin