What is the general solution for cos(x)-3sin(x)=0 ?

The general solution for cos(x)-3sin(x)=0 is x=0.32175…+pin

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

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

x = 0.32175 \dots + πn

Degrees

x = 18.43494 \dots^{\circ} + 18 0^{\circ} n

Solution steps

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

Rewrite using trig identities

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

Divide both sides by

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

\frac{cos ( x ) - 3 sin ( x )}{cos ( x )} = \frac{0}{cos ( x )}

Simplify

1 - \frac{3 sin ( x )}{cos ( x )} = 0

Use the basic trigonometric identity:

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

1 - 3 tan (x) = 0

1 - 3 tan (x) = 0

Move

1

to the right side

1 - 3 tan (x) = 0

Subtract

1

from both sides

1 - 3 tan (x) - 1 = 0 - 1

Simplify

- 3 tan (x) = - 1

- 3 tan (x) = - 1

Divide both sides by

- 3

- 3 tan (x) = - 1

Divide both sides by

- 3

\frac{- 3 tan ( x )}{- 3} = \frac{- 1}{- 3}

Simplify

tan (x) = \frac{1}{3}

tan (x) = \frac{1}{3}

Apply trig inverse properties

tan (x) = \frac{1}{3}

General solutions for

tan (x) = \frac{1}{3}

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

x = arctan (\frac{1}{3}) + πn

x = arctan (\frac{1}{3}) + πn

Show solutions in decimal form

x = 0.32175 \dots + πn

2 cos (4 x) + 3 = 4 cos (2 x)

sinh (y) = 0

2 + 2 cos (θ) = 4

sin^{2} (x) - 2 sin (x) = 3

sin (x + \frac{π}{3}) = \frac{1}{2}

What is the general solution for cos(x)-3sin(x)=0 ?
The general solution for cos(x)-3sin(x)=0 is x=0.32175…+pin