What is the general solution for 0=-2sin(x)+cos(x) ?

The general solution for 0=-2sin(x)+cos(x) is x=0.46364…+pin

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

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

x = 0.46364 \dots + πn

Degrees

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

Solution steps

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

Switch sides

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

Rewrite using trig identities

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

Divide both sides by

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

\frac{- 2 sin ( x ) + cos ( x )}{cos ( x )} = \frac{0}{cos ( x )}

Simplify

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

Use the basic trigonometric identity:

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

- 2 tan (x) + 1 = 0

- 2 tan (x) + 1 = 0

Move

1

to the right side

- 2 tan (x) + 1 = 0

Subtract

1

from both sides

- 2 tan (x) + 1 - 1 = 0 - 1

Simplify

- 2 tan (x) = - 1

- 2 tan (x) = - 1

Divide both sides by

- 2

- 2 tan (x) = - 1

Divide both sides by

- 2

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

Simplify

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

tan (θ) = \frac{7}{6}

2 sin (x) + 5 = 6

sin (2 θ) - cos (2 θ) = 1

cos (θ) = \frac{1}{3}

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

What is the general solution for 0=-2sin(x)+cos(x) ?
The general solution for 0=-2sin(x)+cos(x) is x=0.46364…+pin