What is the general solution for sin(θ)= 4/5 cos(θ) ?

The general solution for sin(θ)= 4/5 cos(θ) is θ=0.67474…+pin

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sin(θ)= 4/5 cos(θ)

sin (θ) = \frac{4}{5} cos (θ)

θ = 0.67474 \dots + πn

Degrees

θ = 38.65980 \dots^{\circ} + 18 0^{\circ} n

Solution steps

sin (θ) = \frac{4}{5} cos (θ)

Rewrite using trig identities

sin (θ) = \frac{4}{5} cos (θ)

Divide both sides by

cos (θ), cos (θ) \neq = 0

\frac{sin ( θ )}{cos ( θ )} = \frac{\frac{4}{5} cos ( θ )}{cos ( θ )}

Simplify

\frac{sin ( θ )}{cos ( θ )} = \frac{4}{5}

Use the basic trigonometric identity:

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

tan (θ) = \frac{4}{5}

tan (θ) = \frac{4}{5}

Apply trig inverse properties

tan (θ) = \frac{4}{5}

General solutions for

tan (θ) = \frac{4}{5}

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

θ = arctan (\frac{4}{5}) + πn

θ = arctan (\frac{4}{5}) + πn

Show solutions in decimal form

θ = 0.67474 \dots + πn

19 = \frac{1}{2} \cdot 7.9 \cdot 6.2 sin (x)

cos (x) = - 0.71

tan (α) = \frac{8}{10}

sin (2 x) + 2 \cdot cos (x) = 0

\frac{6.7}{sin ( 3 3 ^{\circ} )} = \frac{5.4}{sin ( A )}

What is the general solution for sin(θ)= 4/5 cos(θ) ?
The general solution for sin(θ)= 4/5 cos(θ) is θ=0.67474…+pin