What is the general solution for 1032/3145 sin(4x)+2196/3145 cos(4x)=0 ?

The general solution for 1032/3145 sin(4x)+2196/3145 cos(4x)=0 is x=-(1.13148…)/4+(pin)/4

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Popular >

1032/3145 sin(4x)+2196/3145 cos(4x)=0

Solution

\frac{1032}{3145} sin (4 x) + \frac{2196}{3145} cos (4 x) = 0

Solution

x = - \frac{1.13148 \dots}{4} + \frac{πn}{4}

Degrees

x = - 16.20725 \dots^{\circ} + 4 5^{\circ} n

Solution steps

\frac{1032}{3145} sin (4 x) + \frac{2196}{3145} cos (4 x) = 0

Rewrite using trig identities

\frac{1032}{3145} sin (4 x) + \frac{2196}{3145} cos (4 x) = 0

Divide both sides by

cos (4 x), cos (4 x) \neq = 0

\frac{\frac{1032}{3145} sin ( 4 x ) + \frac{2196}{3145} cos ( 4 x )}{cos ( 4 x )} = \frac{0}{cos ( 4 x )}

Simplify

\frac{1032 sin ( 4 x )}{3145 cos ( 4 x )} + \frac{2196}{3145} = 0

Use the basic trigonometric identity:

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

\frac{1032 tan ( 4 x ) + 2196}{3145} = 0

\frac{1032 tan ( 4 x ) + 2196}{3145} = 0

Multiply both sides by

3145

\frac{1032 tan ( 4 x ) + 2196}{3145} = 0

Multiply both sides by

3145

\frac{3145 ( 1032 tan ( 4 x ) + 2196 )}{3145} = 0 \cdot 3145

Simplify

1032 tan (4 x) + 2196 = 0

1032 tan (4 x) + 2196 = 0

Move

2196

to the right side

1032 tan (4 x) + 2196 = 0

Subtract

2196

from both sides

1032 tan (4 x) + 2196 - 2196 = 0 - 2196

Simplify

1032 tan (4 x) = - 2196

1032 tan (4 x) = - 2196

Divide both sides by

1032

1032 tan (4 x) = - 2196

Divide both sides by

1032

\frac{1032 tan ( 4 x )}{1032} = \frac{- 2196}{1032}

Simplify

\frac{1032 tan ( 4 x )}{1032} = \frac{- 2196}{1032}

Simplify

\frac{1032 tan ( 4 x )}{1032} : tan (4 x)

\frac{1032 tan ( 4 x )}{1032}

Divide the numbers:

\frac{1032}{1032} = 1

= tan (4 x)

Simplify

\frac{- 2196}{1032} : - \frac{183}{86}

\frac{- 2196}{1032}

Apply the fraction rule:

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

= - \frac{2196}{1032}

Cancel the common factor:

12

= - \frac{183}{86}

tan (4 x) = - \frac{183}{86}

tan (4 x) = - \frac{183}{86}

tan (4 x) = - \frac{183}{86}

Apply trig inverse properties

tan (4 x) = - \frac{183}{86}

General solutions for

tan (4 x) = - \frac{183}{86}

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

4 x = arctan (- \frac{183}{86}) + πn

4 x = arctan (- \frac{183}{86}) + πn

Solve

4 x = arctan (- \frac{183}{86}) + πn : x = - \frac{arctan ( \frac{183}{86} )}{4} + \frac{πn}{4}

4 x = arctan (- \frac{183}{86}) + πn

Simplify

arctan (- \frac{183}{86}) + πn : - arctan (\frac{183}{86}) + πn

arctan (- \frac{183}{86}) + πn

Use the following property:

arctan (- x) = - arctan (x)

arctan (- \frac{183}{86}) = - arctan (\frac{183}{86})

= - arctan (\frac{183}{86}) + πn

4 x = - arctan (\frac{183}{86}) + πn

Divide both sides by

4

4 x = - arctan (\frac{183}{86}) + πn

Divide both sides by

4

\frac{4 x}{4} = - \frac{arctan ( \frac{183}{86} )}{4} + \frac{πn}{4}

Simplify

x = - \frac{arctan ( \frac{183}{86} )}{4} + \frac{πn}{4}

x = - \frac{arctan ( \frac{183}{86} )}{4} + \frac{πn}{4}

x = - \frac{arctan ( \frac{183}{86} )}{4} + \frac{πn}{4}

Show solutions in decimal form

x = - \frac{1.13148 \dots}{4} + \frac{πn}{4}

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Frequently Asked Questions (FAQ)

What is the general solution for 1032/3145 sin(4x)+2196/3145 cos(4x)=0 ?
The general solution for 1032/3145 sin(4x)+2196/3145 cos(4x)=0 is x=-(1.13148…)/4+(pin)/4