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

The general solution for 3sin(2x)=2cos(2x) is x=(0.58800…)/2+(pin)/2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

x = \frac{0.58800 \dots}{2} + \frac{πn}{2}

Solution steps

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

Rewrite using trig identities

3 tan (2 x) = 2

Divide both sides by

3

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

Apply trig inverse properties

2 x = arctan (\frac{2}{3}) + πn

Solve

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

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

Show solutions in decimal form

x = \frac{0.58800 \dots}{2} + \frac{πn}{2}

cos^{2} (θ) = 3 (1 - sin (θ))

cos (x) = \frac{13}{20}

sin^{2} (x) = 3 cos (x)

2 sin^{2} (x) + sin (x) = 1, 0 \leq x < 2 π

cos (\frac{7 π}{8} - x) = \frac{2}{2}

What is the general solution for 3sin(2x)=2cos(2x) ?
The general solution for 3sin(2x)=2cos(2x) is x=(0.58800…)/2+(pin)/2