What is the general solution for sin(2x)=3cos(2x) ?

The general solution for sin(2x)=3cos(2x) is x=(1.24904…)/2+(pin)/2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

sin(2x)=3cos(2x)

sin (2 x) = 3 cos (2 x)

x = \frac{1.24904 \dots}{2} + \frac{πn}{2}

Solution steps

sin (2 x) = 3 cos (2 x)

Rewrite using trig identities

tan (2 x) = 3

Apply trig inverse properties

2 x = arctan (3) + πn

Solve

2 x = arctan (3) + πn : x = \frac{arctan ( 3 )}{2} + \frac{πn}{2}

x = \frac{arctan ( 3 )}{2} + \frac{πn}{2}

Show solutions in decimal form

x = \frac{1.24904 \dots}{2} + \frac{πn}{2}

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

sec (3 x) = - 1

2 cos^{2} (x) + 1 = 3 cos (x)

cos (x) + 2 = 3 cos (x)

tan (2 θ) = 0

What is the general solution for sin(2x)=3cos(2x) ?
The general solution for sin(2x)=3cos(2x) is x=(1.24904…)/2+(pin)/2