What is the general solution for ((1))/((cot(θ)))=(-(7))/((25)) ?

The general solution for ((1))/((cot(θ)))=(-(7))/((25)) is θ=2.86858…+pin

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((1))/((cot(θ)))=(-(7))/((25))

\frac{( 1 )}{( cot ( θ ) )} = \frac{- ( 7 )}{( 25 )}

θ = 2.86858 \dots + πn

Solution steps

\frac{( 1 )}{( cot ( θ ) )} = \frac{- ( 7 )}{( 25 )}

Cross multiply

25 = - 7 cot (θ)

Switch sides

- 7 cot (θ) = 25

Divide both sides by

- 7

cot (θ) = - \frac{25}{7}

Verify Solutions

Find undefined (singularity) points:

cot (θ) = 0

Combine undefined points with solutions:

cot (θ) = - \frac{25}{7}

Apply trig inverse properties

θ = arccot (- \frac{25}{7}) + πn

Show solutions in decimal form

θ = 2.86858 \dots + πn

tan (θ) = \frac{- 1}{- 2}

sin (θ) = - \frac{1}{3}, \frac{3 π}{2} < θ < 2 π

4 cos (x) = 5 - 1

2 sin^{2} (θ) - 2 sin (θ) = 0

2 - cos (θ) = 2 + sin (θ)

What is the general solution for ((1))/((cot(θ)))=(-(7))/((25)) ?
The general solution for ((1))/((cot(θ)))=(-(7))/((25)) is θ=2.86858…+pin