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

3 sin (x) - cos (2 x) = 1

20 = 15 cos (x) \cdot 2, 47

\frac{[ sin ( x ) + cos ( x ) ]}{cos ( x )} = sin (x) + 1

cos (A) = 0.4639

csc (A) = \frac{9.43}{5}

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