What is the general solution for 4sin(x)=-2cos(x) ?

The general solution for 4sin(x)=-2cos(x) is x=-0.46364…+pin

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4sin(x)=-2cos(x)

4 sin (x) = - 2 cos (x)

x = - 0.46364 \dots + πn

Degrees

x = - 26.56505 \dots^{\circ} + 18 0^{\circ} n

Solution steps

4 sin (x) = - 2 cos (x)

Rewrite using trig identities

4 sin (x) = - 2 cos (x)

Divide both sides by

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

\frac{4 sin ( x )}{cos ( x )} = \frac{- 2 cos ( x )}{cos ( x )}

Simplify

\frac{4 sin ( x )}{cos ( x )} = - 2

Use the basic trigonometric identity:

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

4 tan (x) = - 2

4 tan (x) = - 2

Divide both sides by

4

4 tan (x) = - 2

Divide both sides by

4

\frac{4 tan ( x )}{4} = \frac{- 2}{4}

Simplify

\frac{4 tan ( x )}{4} = \frac{- 2}{4}

Simplify

\frac{4 tan ( x )}{4} : tan (x)

\frac{4 tan ( x )}{4}

Divide the numbers:

\frac{4}{4} = 1

= tan (x)

Simplify

\frac{- 2}{4} : - \frac{1}{2}

\frac{- 2}{4}

Apply the fraction rule:

\frac{- a}{b} = - \frac{a}{b}

= - \frac{2}{4}

Cancel the common factor:

2

= - \frac{1}{2}

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

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

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

Apply trig inverse properties

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

General solutions for

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

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

x = arctan (- \frac{1}{2}) + πn

x = arctan (- \frac{1}{2}) + πn

Show solutions in decimal form

x = - 0.46364 \dots + πn

3 sin (2 x) = 1.5

sin (2 x - 5 0^{\circ}) = - \frac{1}{2}

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

cos (x) = cos (3 \cdot x) + 2 \cdot sin (2 \cdot x)

- 2 sin (x) + 3 cos (x) = 0

What is the general solution for 4sin(x)=-2cos(x) ?
The general solution for 4sin(x)=-2cos(x) is x=-0.46364…+pin