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

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

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

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

x = 0.58800 \dots + πn

Degrees

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

Solution steps

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

Rewrite using trig identities

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

Divide both sides by

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

\frac{\frac{s i n ( x )}{2}}{cos ( x )} = \frac{\frac{c o s ( x )}{3}}{cos ( x )}

Simplify

\frac{sin ( x )}{2 cos ( x )} = \frac{1}{3}

Use the basic trigonometric identity:

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

\frac{tan ( x )}{2} = \frac{1}{3}

\frac{tan ( x )}{2} = \frac{1}{3}

Multiply both sides by

2

\frac{tan ( x )}{2} = \frac{1}{3}

Multiply both sides by

2

\frac{2 tan ( x )}{2} = \frac{1 \cdot 2}{3}

Simplify

\frac{2 tan ( x )}{2} = \frac{1 \cdot 2}{3}

Simplify

\frac{2 tan ( x )}{2} : tan (x)

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

Divide the numbers:

\frac{2}{2} = 1

= tan (x)

Simplify

\frac{1 \cdot 2}{3} : \frac{2}{3}

\frac{1 \cdot 2}{3}

Multiply the numbers:

1 \cdot 2 = 2

= \frac{2}{3}

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

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) - 2 = 0, \frac{π}{2} < θ < \frac{3 π}{2}

9 sin (x) + 6 cos (x) = 10

- 2 cos^{2} (x) - sin (x) + 1 = 0

cos (x) = \frac{4}{21}

11 - 12 cos^{2} (θ) = 0

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