What is the general solution for 6sin(θ)=2.5cos(θ) ?

The general solution for 6sin(θ)=2.5cos(θ) is θ=0.39479…+pin

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6sin(θ)=2.5cos(θ)

6 sin (θ) = 2.5 cos (θ)

θ = 0.39479 \dots + πn

Degrees

θ = 22.61986 \dots^{\circ} + 18 0^{\circ} n

Solution steps

6 sin (θ) = 2.5 cos (θ)

Rewrite using trig identities

6 sin (θ) = 2.5 cos (θ)

Divide both sides by

cos (θ), cos (θ) \neq = 0

\frac{6 sin ( θ )}{cos ( θ )} = \frac{2.5 cos ( θ )}{cos ( θ )}

Simplify

\frac{6 sin ( θ )}{cos ( θ )} = 2.5

Use the basic trigonometric identity:

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

6 tan (θ) = 2.5

6 tan (θ) = 2.5

Divide both sides by

6

6 tan (θ) = 2.5

Divide both sides by

6

\frac{6 tan ( θ )}{6} = \frac{2.5}{6}

Simplify

tan (θ) = 0.41666 \dots

tan (θ) = 0.41666 \dots

Apply trig inverse properties

tan (θ) = 0.41666 \dots

General solutions for

tan (θ) = 0.41666 \dots

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

θ = arctan (0.41666 \dots) + πn

θ = arctan (0.41666 \dots) + πn

Show solutions in decimal form

θ = 0.39479 \dots + πn

tan^{3} (x) + tan^{2} (x) - tan (x) - 1 = 0

tan (θ) = \frac{- 4 3}{4}

3 sin (x) - cos (x) = 3, 0 \leq x \leq 2 π

- 1 + 3 sin (x) = - 1 + 4 sin (x)

cos (x) = \frac{6}{25}

What is the general solution for 6sin(θ)=2.5cos(θ) ?
The general solution for 6sin(θ)=2.5cos(θ) is θ=0.39479…+pin