What is the general solution for 6cos(2x)+8sin(2x)=0 ?

The general solution for 6cos(2x)+8sin(2x)=0 is x=-(0.64350…)/2+(pin)/2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

6cos(2x)+8sin(2x)=0

Solution

6 cos (2 x) + 8 sin (2 x) = 0

Solution

x = - \frac{0.64350 \dots}{2} + \frac{πn}{2}

Degrees

x = - 18.43494 \dots^{\circ} + 9 0^{\circ} n

Solution steps

6 cos (2 x) + 8 sin (2 x) = 0

Rewrite using trig identities

6 cos (2 x) + 8 sin (2 x) = 0

Divide both sides by

cos (2 x), cos (2 x) \neq = 0

\frac{6 cos ( 2 x ) + 8 sin ( 2 x )}{cos ( 2 x )} = \frac{0}{cos ( 2 x )}

Simplify

6 + \frac{8 sin ( 2 x )}{cos ( 2 x )} = 0

Use the basic trigonometric identity:

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

6 + 8 tan (2 x) = 0

6 + 8 tan (2 x) = 0

Move

6

to the right side

6 + 8 tan (2 x) = 0

Subtract

6

from both sides

6 + 8 tan (2 x) - 6 = 0 - 6

Simplify

8 tan (2 x) = - 6

8 tan (2 x) = - 6

Divide both sides by

8

8 tan (2 x) = - 6

Divide both sides by

8

\frac{8 tan ( 2 x )}{8} = \frac{- 6}{8}

Simplify

\frac{8 tan ( 2 x )}{8} = \frac{- 6}{8}

Simplify

\frac{8 tan ( 2 x )}{8} : tan (2 x)

\frac{8 tan ( 2 x )}{8}

Divide the numbers:

\frac{8}{8} = 1

= tan (2 x)

Simplify

\frac{- 6}{8} : - \frac{3}{4}

\frac{- 6}{8}

Apply the fraction rule:

\frac{- a}{b} = - \frac{a}{b}

= - \frac{6}{8}

Cancel the common factor:

2

= - \frac{3}{4}

tan (2 x) = - \frac{3}{4}

tan (2 x) = - \frac{3}{4}

tan (2 x) = - \frac{3}{4}

Apply trig inverse properties

tan (2 x) = - \frac{3}{4}

General solutions for

tan (2 x) = - \frac{3}{4}

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

2 x = arctan (- \frac{3}{4}) + πn

2 x = arctan (- \frac{3}{4}) + πn

Solve

2 x = arctan (- \frac{3}{4}) + πn : x = - \frac{arctan ( \frac{3}{4} )}{2} + \frac{πn}{2}

2 x = arctan (- \frac{3}{4}) + πn

Simplify

arctan (- \frac{3}{4}) + πn : - arctan (\frac{3}{4}) + πn

arctan (- \frac{3}{4}) + πn

Use the following property:

arctan (- x) = - arctan (x)

arctan (- \frac{3}{4}) = - arctan (\frac{3}{4})

= - arctan (\frac{3}{4}) + πn

2 x = - arctan (\frac{3}{4}) + πn

Divide both sides by

2

2 x = - arctan (\frac{3}{4}) + πn

Divide both sides by

2

\frac{2 x}{2} = - \frac{arctan ( \frac{3}{4} )}{2} + \frac{πn}{2}

Simplify

x = - \frac{arctan ( \frac{3}{4} )}{2} + \frac{πn}{2}

x = - \frac{arctan ( \frac{3}{4} )}{2} + \frac{πn}{2}

x = - \frac{arctan ( \frac{3}{4} )}{2} + \frac{πn}{2}

Show solutions in decimal form

x = - \frac{0.64350 \dots}{2} + \frac{πn}{2}

Popular Examples

cos(x)= 8/17 ,sin(x)

cos (x) = \frac{8}{17}, sin (x)

(50)/(sin(105))=(20)/(sin(x))

\frac{50}{sin ( 10 5 ^{\circ} )} = \frac{20}{sin ( x )}

solvefor x,sin^2(x)=(5m-5)/2 solve for

x, sin^{2} (x) = \frac{5 m - 5}{2}

csc(θ)=-1.343

csc (θ) = - 1.343

csc(θ)=-3/2 ,pi<θ<(3pi)/2 ,sin(θ)

csc (θ) = - \frac{3}{2}, π < θ < \frac{3 π}{2}, sin (θ)

Frequently Asked Questions (FAQ)

What is the general solution for 6cos(2x)+8sin(2x)=0 ?
The general solution for 6cos(2x)+8sin(2x)=0 is x=-(0.64350…)/2+(pin)/2