What is the general solution for 2cos(x)+3sin(x)=0 ?

The general solution for 2cos(x)+3sin(x)=0 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 >

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

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

x = - 0.58800 \dots + πn

Degrees

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

Solution steps

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

sec (\frac{x}{5}) = 10

csc (x) = - 3

csc (x) = - 5

csc^{2} (θ) + 1 = cot^{2} (θ)

csc^{2} (θ) = 1

What is the general solution for 2cos(x)+3sin(x)=0 ?
The general solution for 2cos(x)+3sin(x)=0 is x=-0.58800…+pin