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

The general solution for -2cos(x)=sin(x) is x=-1.10714…+pin

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-2cos(x)=sin(x)

- 2 cos (x) = sin (x)

x = - 1.10714 \dots + πn

Degrees

x = - 63.43494 \dots^{\circ} + 18 0^{\circ} n

Solution steps

- 2 cos (x) = sin (x)

Rewrite using trig identities

- 2 cos (x) = sin (x)

Divide both sides by

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

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

Simplify

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

Use the basic trigonometric identity:

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

- 2 = tan (x)

Switch sides

tan (x) = - 2

tan (x) = - 2

Apply trig inverse properties

tan (x) = - 2

General solutions for

tan (x) = - 2

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

x = arctan (- 2) + πn

x = arctan (- 2) + πn

Show solutions in decimal form

x = - 1.10714 \dots + πn

sin (x) = - 0.9781

tan (x) = 3.73

tan (θ) = - \frac{2}{5}, sin (θ) > 0

sin (4 θ) = \frac{3}{2}, 0 \leq θ < 2 π

x, z = cot (4 x^{3} y^{6} - 4 x^{4})

What is the general solution for -2cos(x)=sin(x) ?
The general solution for -2cos(x)=sin(x) is x=-1.10714…+pin