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

The general solution for 3sin(x)=2cos(x) is x=0.58800…+pin

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3sin(x)=2cos(x)

3 sin (x) = 2 cos (x)

x = 0.58800 \dots + πn

Degrees

x = 33.69006 \dots^{\circ} + 18 0^{\circ} n

Solution steps

3 sin (x) = 2 cos (x)

Rewrite using trig identities

3 sin (x) = 2 cos (x)

Divide both sides by

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

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

Simplify

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

Use the basic trigonometric identity:

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

3 tan (x) = 2

3 tan (x) = 2

Divide both sides by

3

3 tan (x) = 2

Divide both sides by

3

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

Simplify

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

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

Apply trig inverse properties

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

General solutions for

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

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

x = arctan (\frac{2}{3}) + πn

x = arctan (\frac{2}{3}) + πn

Show solutions in decimal form

x = 0.58800 \dots + πn

5 cot (x) + 2 csc^{2} (x) = 5

cos (2 x) = \frac{4}{5}

tan (x) = \frac{160}{85}

sin (x) a = π

sin (5 x) + sin (x) = 0

What is the general solution for 3sin(x)=2cos(x) ?
The general solution for 3sin(x)=2cos(x) is x=0.58800…+pin