What is the general solution for -8sin(2x)-14cos(2x)=0 ?

The general solution for -8sin(2x)-14cos(2x)=0 is x=-(1.05165…)/2+(pin)/2

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Popular >

-8sin(2x)-14cos(2x)=0

Solution

- 8 sin (2 x) - 14 cos (2 x) = 0

Solution

x = - \frac{1.05165 \dots}{2} + \frac{πn}{2}

Degrees

x = - 30.12755 \dots^{\circ} + 9 0^{\circ} n

Solution steps

- 8 sin (2 x) - 14 cos (2 x) = 0

Rewrite using trig identities

- 8 sin (2 x) - 14 cos (2 x) = 0

Divide both sides by

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

\frac{- 8 sin ( 2 x ) - 14 cos ( 2 x )}{cos ( 2 x )} = \frac{0}{cos ( 2 x )}

Simplify

- \frac{8 sin ( 2 x )}{cos ( 2 x )} - 14 = 0

Use the basic trigonometric identity:

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

- 8 tan (2 x) - 14 = 0

- 8 tan (2 x) - 14 = 0

Move

14

to the right side

- 8 tan (2 x) - 14 = 0

Add

14

to both sides

- 8 tan (2 x) - 14 + 14 = 0 + 14

Simplify

- 8 tan (2 x) = 14

- 8 tan (2 x) = 14

Divide both sides by

- 8

- 8 tan (2 x) = 14

Divide both sides by

- 8

\frac{- 8 tan ( 2 x )}{- 8} = \frac{14}{- 8}

Simplify

\frac{- 8 tan ( 2 x )}{- 8} = \frac{14}{- 8}

Simplify

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

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

Apply the fraction rule:

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

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

Divide the numbers:

\frac{8}{8} = 1

= tan (2 x)

Simplify

\frac{14}{- 8} : - \frac{7}{4}

\frac{14}{- 8}

Apply the fraction rule:

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

= - \frac{14}{8}

Cancel the common factor:

2

= - \frac{7}{4}

tan (2 x) = - \frac{7}{4}

tan (2 x) = - \frac{7}{4}

tan (2 x) = - \frac{7}{4}

Apply trig inverse properties

tan (2 x) = - \frac{7}{4}

General solutions for

tan (2 x) = - \frac{7}{4}

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

2 x = arctan (- \frac{7}{4}) + πn

2 x = arctan (- \frac{7}{4}) + πn

Solve

2 x = arctan (- \frac{7}{4}) + πn : x = - \frac{arctan ( \frac{7}{4} )}{2} + \frac{πn}{2}

2 x = arctan (- \frac{7}{4}) + πn

Simplify

arctan (- \frac{7}{4}) + πn : - arctan (\frac{7}{4}) + πn

arctan (- \frac{7}{4}) + πn

Use the following property:

arctan (- x) = - arctan (x)

arctan (- \frac{7}{4}) = - arctan (\frac{7}{4})

= - arctan (\frac{7}{4}) + πn

2 x = - arctan (\frac{7}{4}) + πn

Divide both sides by

2

2 x = - arctan (\frac{7}{4}) + πn

Divide both sides by

2

\frac{2 x}{2} = - \frac{arctan ( \frac{7}{4} )}{2} + \frac{πn}{2}

Simplify

x = - \frac{arctan ( \frac{7}{4} )}{2} + \frac{πn}{2}

x = - \frac{arctan ( \frac{7}{4} )}{2} + \frac{πn}{2}

x = - \frac{arctan ( \frac{7}{4} )}{2} + \frac{πn}{2}

Show solutions in decimal form

x = - \frac{1.05165 \dots}{2} + \frac{πn}{2}

Graph

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Frequently Asked Questions (FAQ)

What is the general solution for -8sin(2x)-14cos(2x)=0 ?
The general solution for -8sin(2x)-14cos(2x)=0 is x=-(1.05165…)/2+(pin)/2