What is the general solution for sin(θ)= 3/5 cos(θ) ?

The general solution for sin(θ)= 3/5 cos(θ) is θ=0.54041…+pin

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sin(θ)= 3/5 cos(θ)

sin (θ) = \frac{3}{5} cos (θ)

θ = 0.54041 \dots + πn

Degrees

θ = 30.96375 \dots^{\circ} + 18 0^{\circ} n

Solution steps

sin (θ) = \frac{3}{5} cos (θ)

Rewrite using trig identities

sin (θ) = \frac{3}{5} cos (θ)

Divide both sides by

cos (θ), cos (θ) \neq = 0

\frac{sin ( θ )}{cos ( θ )} = \frac{\frac{3}{5} cos ( θ )}{cos ( θ )}

Simplify

\frac{sin ( θ )}{cos ( θ )} = \frac{3}{5}

Use the basic trigonometric identity:

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

tan (θ) = \frac{3}{5}

tan (θ) = \frac{3}{5}

Apply trig inverse properties

tan (θ) = \frac{3}{5}

General solutions for

tan (θ) = \frac{3}{5}

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

θ = arctan (\frac{3}{5}) + πn

θ = arctan (\frac{3}{5}) + πn

Show solutions in decimal form

θ = 0.54041 \dots + πn

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

sin (a) = \frac{5}{6}

2 sin^{2} (x) cos (x) = cos (x)

cos (2 θ) + sin (θ) + 2 = 0

cos (x) = \frac{10}{50}

What is the general solution for sin(θ)= 3/5 cos(θ) ?
The general solution for sin(θ)= 3/5 cos(θ) is θ=0.54041…+pin