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

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

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

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

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

Solution steps

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

Rewrite using trig identities

5 tan (2 x) = 3

Divide both sides by

5

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

Apply trig inverse properties

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}

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

Show solutions in decimal form

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

4 cos (3 x - 20) = 1

0 = 1.9 cos (0.1 t) - 1.25 sin (0.2 t)

sin (\frac{x}{4}) = \frac{3}{2}

cos (θ) = \frac{- 3 + ( - 6 )}{( 9 ) ( 18 )}

sin (\frac{6}{x}) = 36

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