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

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

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cos(x)=3sin(x)

cos (x) = 3 sin (x)

x = 0.32175 \dots + πn

Degrees

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

Solution steps

cos (x) = 3 sin (x)

Rewrite using trig identities

cos (x) = 3 sin (x)

Divide both sides by

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

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

Simplify

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

Use the basic trigonometric identity:

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

1 = 3 tan (x)

Switch sides

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

tan (23 θ) + cot (23 θ) = \frac{4}{3}

tan^{2} (x) + 1 = sec (x)

\frac{3}{16} = 1 (cos (0)) (cos (3 0^{\circ})) (cos (x - 3 0^{\circ}))

cos (x) - 2 = - 5 + 2

1 + sec^{2} (x) = tan (x)

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