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

Solution steps

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

Switch sides

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

Rewrite using trig identities

- 2 tan (x) + 1 = 0

Move

1

to the right side

- 2 tan (x) = - 1

Divide both sides by

- 2

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

Apply trig inverse properties

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