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

The general solution for 3cos(θ)=sin(θ) is θ=1.24904…+pin

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3cos(θ)=sin(θ)

3 cos (θ) = sin (θ)

θ = 1.24904 \dots + πn

Degrees

θ = 71.56505 \dots^{\circ} + 18 0^{\circ} n

Solution steps

3 cos (θ) = sin (θ)

Rewrite using trig identities

3 cos (θ) = sin (θ)

Divide both sides by

cos (θ), cos (θ) \neq = 0

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

Simplify

3 = \frac{sin ( θ )}{cos ( θ )}

Use the basic trigonometric identity:

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

3 = tan (θ)

Switch sides

tan (θ) = 3

tan (θ) = 3

Apply trig inverse properties

tan (θ) = 3

General solutions for

tan (θ) = 3

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

θ = arctan (3) + πn

θ = arctan (3) + πn

Show solutions in decimal form

θ = 1.24904 \dots + πn

- 4 cos^{(2)} (x) + 42 sin (x) + 6 = 0

3 tan^{2} (x) - 10 tan (x) + 7 = 0

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

\frac{1}{2} cot (x) = cos (x)

θ, 2 cos (θ) + 1 = 0

What is the general solution for 3cos(θ)=sin(θ) ?
The general solution for 3cos(θ)=sin(θ) is θ=1.24904…+pin