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

The general solution for 3sin(2x)=2 is x=(0.72972…)/2+pin,x= pi/2-(0.72972…)/2+pin

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

3sin(2x)=2

3 sin (2 x) = 2

x = \frac{0.72972 \dots}{2} + πn, x = \frac{π}{2} - \frac{0.72972 \dots}{2} + πn

Solution steps

3 sin (2 x) = 2

Divide both sides by

3

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

Apply trig inverse properties

2 x = arcsin (\frac{2}{3}) + 2 πn, 2 x = π - arcsin (\frac{2}{3}) + 2 πn

Solve

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

Solve

2 x = π - arcsin (\frac{2}{3}) + 2 πn : x = \frac{π}{2} - \frac{arcsin ( \frac{2}{3} )}{2} + πn

x = \frac{arcsin ( \frac{2}{3} )}{2} + πn, x = \frac{π}{2} - \frac{arcsin ( \frac{2}{3} )}{2} + πn

Show solutions in decimal form

x = \frac{0.72972 \dots}{2} + πn, x = \frac{π}{2} - \frac{0.72972 \dots}{2} + πn

x, cos (2 x) = 0

sec (θ) = \frac{3}{2}

6 cos (θ) + 3 = 0

sin^{2} (x) + 5 sin (x) + 6 = 0

- 6 tan^{2} (θ) + 11 tan (θ) - 6 = - 2 tan (θ)

What is the general solution for 3sin(2x)=2 ?
The general solution for 3sin(2x)=2 is x=(0.72972…)/2+pin,x= pi/2-(0.72972…)/2+pin