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

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

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2cos(x)=3sin(x)

2 cos (x) = 3 sin (x)

x = 0.58800 \dots + πn

Degrees

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

Solution steps

2 cos (x) = 3 sin (x)

Rewrite using trig identities

2 cos (x) = 3 sin (x)

Divide both sides by

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

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

Simplify

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

Use the basic trigonometric identity:

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

2 = 3 tan (x)

Switch sides

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

4 sin^{2} (θ) - 8 cos (θ) + 1 = 0

sin (x) cos (\frac{π}{7}) - sin (\frac{π}{7}) cos (x) = \frac{2}{2}

20 sin (t) cos (t) = - 16 cos (t)

cos (x + 2 5^{\circ}) sec (6 5^{\circ} - x) = 1

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

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