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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

x = - 0.58800 \dots + πn

Degrees

x = - 33.69006 \dots^{\circ} + 18 0^{\circ} n

Solution steps

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

Subtract

cos (x) - 2 sin (x)

from both sides

2 cos (x) + 3 sin (x) = 0

Rewrite using trig identities

2 cos (x) + 3 sin (x) = 0

Divide both sides by

cos (x), cos (x) \neq = 0

\frac{2 cos ( x ) + 3 sin ( x )}{cos ( x )} = \frac{0}{cos ( x )}

Simplify

2 + \frac{3 sin ( x )}{cos ( x )} = 0

Use the basic trigonometric identity:

\frac{sin ( x )}{cos ( x )} = tan (x)

2 + 3 tan (x) = 0

2 + 3 tan (x) = 0

Move

2

to the right side

2 + 3 tan (x) = 0

Subtract

2

from both sides

2 + 3 tan (x) - 2 = 0 - 2

Simplify

3 tan (x) = - 2

3 tan (x) = - 2

Divide both sides by

3

3 tan (x) = - 2

Divide both sides by

3

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

Simplify

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

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

Apply trig inverse properties

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

General solutions for

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

tan (x) = - a \Rightarrow x = arctan (- a) + πn

x = arctan (- \frac{2}{3}) + πn

x = arctan (- \frac{2}{3}) + πn

Show solutions in decimal form

x = - 0.58800 \dots + πn

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

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

3 cos (a) - 1 = 0

tan^{2} (x) + tan (x) + cot (x) + cot^{2} (x) = 4

tan (a) = 0

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