What is the general solution for 3sin(θ)=4cos(θ) ?

The general solution for 3sin(θ)=4cos(θ) is θ=0.92729…+pin

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3sin(θ)=4cos(θ)

3 sin (θ) = 4 cos (θ)

θ = 0.92729 \dots + πn

Degrees

θ = 53.13010 \dots^{\circ} + 18 0^{\circ} n

Solution steps

3 sin (θ) = 4 cos (θ)

Rewrite using trig identities

3 sin (θ) = 4 cos (θ)

Divide both sides by

cos (θ), cos (θ) \neq = 0

\frac{3 sin ( θ )}{cos ( θ )} = \frac{4 cos ( θ )}{cos ( θ )}

Simplify

\frac{3 sin ( θ )}{cos ( θ )} = 4

Use the basic trigonometric identity:

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

3 tan (θ) = 4

3 tan (θ) = 4

Divide both sides by

3

3 tan (θ) = 4

Divide both sides by

3

\frac{3 tan ( θ )}{3} = \frac{4}{3}

Simplify

tan (θ) = \frac{4}{3}

tan (θ) = \frac{4}{3}

Apply trig inverse properties

tan (θ) = \frac{4}{3}

General solutions for

tan (θ) = \frac{4}{3}

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

θ = arctan (\frac{4}{3}) + πn

θ = arctan (\frac{4}{3}) + πn

Show solutions in decimal form

θ = 0.92729 \dots + πn

300 = 400 + 200 cos (\frac{π t}{12})

- 6 cos^{2} (θ) = - cos (θ) - 2

2 0^{2} = 1 3^{2} + 9^{2} - 2 (13) (9) \cdot cos (a)

t, 4 cos (2 t) + 1 = 3

cos (2 x) - 3 cos (- x) + 2 = 0

What is the general solution for 3sin(θ)=4cos(θ) ?
The general solution for 3sin(θ)=4cos(θ) is θ=0.92729…+pin