What is the general solution for 3sin(2θ)=2cos(2θ),0<= 2θ<720 ?

The general solution for 3sin(2θ)=2cos(2θ),0<= 2θ<720 is No Solution for θ\in\mathbb{R}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

3sin(2θ)=2cos(2θ),0<= 2θ<720

3 sin (2 θ) = 2 cos (2 θ), 0^{\circ} \leq 2 θ < 72 0^{\circ}

No Solution for θ \in R

Solution steps

3 sin (2 θ) = 2 cos (2 θ), 0^{\circ} \leq 2 θ < 72 0^{\circ}

Rewrite using trig identities

3 tan (2 θ) = 2

Divide both sides by

3

tan (2 θ) = \frac{2}{3}

Apply trig inverse properties

2 θ = arctan (\frac{2}{3}) + 18 0^{\circ} n

Solve

2 θ = arctan (\frac{2}{3}) + 18 0^{\circ} n : θ = \frac{arctan ( \frac{2}{3} )}{2} + \frac{18 0 ^{\circ} n}{2}

θ = \frac{arctan ( \frac{2}{3} )}{2} + \frac{18 0 ^{\circ} n}{2}

Solutions for the range

0 \leq 2 θ < 72 0^{\circ}

No Solution for θ \in R

csc (x) + 2 = 0

sin (x) - sin^{2} (x) = 0

sin (x) = - \frac{3}{13}

sin (α) = - \frac{1}{2}

cos (x) = \frac{11}{20}

What is the general solution for 3sin(2θ)=2cos(2θ),0<= 2θ<720 ?
The general solution for 3sin(2θ)=2cos(2θ),0<= 2θ<720 is No Solution for θ\in\mathbb{R}