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

The general solution for 5sin(2x)=2cos(2x) is x=(0.38050…)/2+(pin)/2

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5sin(2x)=2cos(2x)

5 sin (2 x) = 2 cos (2 x)

x = \frac{0.38050 \dots}{2} + \frac{πn}{2}

Degrees

x = 10.90070 \dots^{\circ} + 9 0^{\circ} n

Solution steps

5 sin (2 x) = 2 cos (2 x)

Rewrite using trig identities

5 sin (2 x) = 2 cos (2 x)

Divide both sides by

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

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

Simplify

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

Use the basic trigonometric identity:

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

5 tan (2 x) = 2

5 tan (2 x) = 2

Divide both sides by

5

5 tan (2 x) = 2

Divide both sides by

5

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

Simplify

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

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

Apply trig inverse properties

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

General solutions for

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

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

2 x = arctan (\frac{2}{5}) + πn

2 x = arctan (\frac{2}{5}) + πn

Solve

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

2 x = arctan (\frac{2}{5}) + πn

Divide both sides by

2

2 x = arctan (\frac{2}{5}) + πn

Divide both sides by

2

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

Simplify

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

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

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

Show solutions in decimal form

x = \frac{0.38050 \dots}{2} + \frac{πn}{2}

tan (2 θ - 1 0^{\circ}) = cot (θ)

sinh (x) = 4

2 cos^{2} (θ) - 3 cos (θ) + 1 = 0, 0 \leq θ < 2 π

cos (x) sin (x) = 1

24 arctan (x) = 4 π

What is the general solution for 5sin(2x)=2cos(2x) ?
The general solution for 5sin(2x)=2cos(2x) is x=(0.38050…)/2+(pin)/2