What is the general solution for solvefor x,-44sin(2x)+42cos(2x)=0 ?

The general solution for solvefor x,-44sin(2x)+42cos(2x)=0 is x=(0.76214…)/2+(pin)/2

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Popular >

solvefor x,-44sin(2x)+42cos(2x)=0

Solution

solve for

x, - 44 sin (2 x) + 42 cos (2 x) = 0

Solution

x = \frac{0.76214 \dots}{2} + \frac{πn}{2}

Degrees

x = 21.83389 \dots^{\circ} + 9 0^{\circ} n

Solution steps

- 44 sin (2 x) + 42 cos (2 x) = 0

Rewrite using trig identities

- 44 sin (2 x) + 42 cos (2 x) = 0

Divide both sides by

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

\frac{- 44 sin ( 2 x ) + 42 cos ( 2 x )}{cos ( 2 x )} = \frac{0}{cos ( 2 x )}

Simplify

- \frac{44 sin ( 2 x )}{cos ( 2 x )} + 42 = 0

Use the basic trigonometric identity:

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

- 44 tan (2 x) + 42 = 0

- 44 tan (2 x) + 42 = 0

Move

42

to the right side

- 44 tan (2 x) + 42 = 0

Subtract

42

from both sides

- 44 tan (2 x) + 42 - 42 = 0 - 42

Simplify

- 44 tan (2 x) = - 42

- 44 tan (2 x) = - 42

Divide both sides by

- 44

- 44 tan (2 x) = - 42

Divide both sides by

- 44

\frac{- 44 tan ( 2 x )}{- 44} = \frac{- 42}{- 44}

Simplify

\frac{- 44 tan ( 2 x )}{- 44} = \frac{- 42}{- 44}

Simplify

\frac{- 44 tan ( 2 x )}{- 44} : tan (2 x)

\frac{- 44 tan ( 2 x )}{- 44}

Apply the fraction rule:

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

= \frac{44 tan ( 2 x )}{44}

Divide the numbers:

\frac{44}{44} = 1

= tan (2 x)

Simplify

\frac{- 42}{- 44} : \frac{21}{22}

\frac{- 42}{- 44}

Apply the fraction rule:

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

= \frac{42}{44}

Cancel the common factor:

2

= \frac{21}{22}

tan (2 x) = \frac{21}{22}

tan (2 x) = \frac{21}{22}

tan (2 x) = \frac{21}{22}

Apply trig inverse properties

tan (2 x) = \frac{21}{22}

General solutions for

tan (2 x) = \frac{21}{22}

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

2 x = arctan (\frac{21}{22}) + πn

2 x = arctan (\frac{21}{22}) + πn

Solve

2 x = arctan (\frac{21}{22}) + πn : x = \frac{arctan ( \frac{21}{22} )}{2} + \frac{πn}{2}

2 x = arctan (\frac{21}{22}) + πn

Divide both sides by

2

2 x = arctan (\frac{21}{22}) + πn

Divide both sides by

2

\frac{2 x}{2} = \frac{arctan ( \frac{21}{22} )}{2} + \frac{πn}{2}

Simplify

x = \frac{arctan ( \frac{21}{22} )}{2} + \frac{πn}{2}

x = \frac{arctan ( \frac{21}{22} )}{2} + \frac{πn}{2}

x = \frac{arctan ( \frac{21}{22} )}{2} + \frac{πn}{2}

Show solutions in decimal form

x = \frac{0.76214 \dots}{2} + \frac{πn}{2}

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Frequently Asked Questions (FAQ)

What is the general solution for solvefor x,-44sin(2x)+42cos(2x)=0 ?
The general solution for solvefor x,-44sin(2x)+42cos(2x)=0 is x=(0.76214…)/2+(pin)/2