What is the general solution for 5sin(2x)+3cos(2x)=0 ?

The general solution for 5sin(2x)+3cos(2x)=0 is x=-(0.54041…)/2+(pin)/2

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Popular >

5sin(2x)+3cos(2x)=0

Solution

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

Solution

x = - \frac{0.54041 \dots}{2} + \frac{πn}{2}

Degrees

x = - 15.48187 \dots^{\circ} + 9 0^{\circ} n

Solution steps

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

Rewrite using trig identities

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

Divide both sides by

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

\frac{5 sin ( 2 x ) + 3 cos ( 2 x )}{cos ( 2 x )} = \frac{0}{cos ( 2 x )}

Simplify

\frac{5 sin ( 2 x )}{cos ( 2 x )} + 3 = 0

Use the basic trigonometric identity:

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

5 tan (2 x) + 3 = 0

5 tan (2 x) + 3 = 0

Move

3

to the right side

5 tan (2 x) + 3 = 0

Subtract

3

from both sides

5 tan (2 x) + 3 - 3 = 0 - 3

Simplify

5 tan (2 x) = - 3

5 tan (2 x) = - 3

Divide both sides by

5

5 tan (2 x) = - 3

Divide both sides by

5

\frac{5 tan ( 2 x )}{5} = \frac{- 3}{5}

Simplify

tan (2 x) = - \frac{3}{5}

tan (2 x) = - \frac{3}{5}

Apply trig inverse properties

tan (2 x) = - \frac{3}{5}

General solutions for

tan (2 x) = - \frac{3}{5}

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

2 x = arctan (- \frac{3}{5}) + πn

2 x = arctan (- \frac{3}{5}) + πn

Solve

2 x = arctan (- \frac{3}{5}) + πn : x = - \frac{arctan ( \frac{3}{5} )}{2} + \frac{πn}{2}

2 x = arctan (- \frac{3}{5}) + πn

Simplify

arctan (- \frac{3}{5}) + πn : - arctan (\frac{3}{5}) + πn

arctan (- \frac{3}{5}) + πn

Use the following property:

arctan (- x) = - arctan (x)

arctan (- \frac{3}{5}) = - arctan (\frac{3}{5})

= - arctan (\frac{3}{5}) + πn

2 x = - arctan (\frac{3}{5}) + πn

Divide both sides by

2

2 x = - arctan (\frac{3}{5}) + πn

Divide both sides by

2

\frac{2 x}{2} = - \frac{arctan ( \frac{3}{5} )}{2} + \frac{πn}{2}

Simplify

x = - \frac{arctan ( \frac{3}{5} )}{2} + \frac{πn}{2}

x = - \frac{arctan ( \frac{3}{5} )}{2} + \frac{πn}{2}

x = - \frac{arctan ( \frac{3}{5} )}{2} + \frac{πn}{2}

Show solutions in decimal form

x = - \frac{0.54041 \dots}{2} + \frac{πn}{2}

Popular Examples

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x, sin (2 x) - sin (x) = 0

solvefor x,sin(x^e)+cos(y^e)=1 solve for

x, sin (x^{e}) + cos (y^{e}) = 1

sin^2(x)+3cos(x)-1=2

sin^{2} (x) + 3 cos (x) - 1 = 2

cot^2(θ)-3csc(θ)+3=0

cot^{2} (θ) - 3 csc (θ) + 3 = 0

solvefor x,arctan(x)+arctan(y)= pi/2 solve for

x, arctan (x) + arctan (y) = \frac{π}{2}

Frequently Asked Questions (FAQ)

What is the general solution for 5sin(2x)+3cos(2x)=0 ?
The general solution for 5sin(2x)+3cos(2x)=0 is x=-(0.54041…)/2+(pin)/2