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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Popular >

((1))/((cot(θ)))=(-(7))/((25))

Solution

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

Solution

θ = 2.86858 \dots + πn

Degrees

θ = 164.35775 \dots^{\circ} + 18 0^{\circ} n

Solution steps

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

Cross multiply

\frac{1}{cot ( θ )} = \frac{- 7}{25}

Apply fraction cross multiply: if

\frac{a}{b} = \frac{c}{d}

then

a \cdot d = b \cdot c

1 \cdot 25 = cot (θ) (- 7)

Simplify

1 \cdot 25 = cot (θ) (- 7)

Simplify

1 \cdot 25 : 25

1 \cdot 25

Multiply the numbers:

1 \cdot 25 = 25

= 25

Simplify

cot (θ) (- 7) : - 7 cot (θ)

cot (θ) (- 7)

Remove parentheses:

(- a) = - a

= - cot (θ) \cdot 7

25 = - 7 cot (θ)

25 = - 7 cot (θ)

25 = - 7 cot (θ)

Switch sides

- 7 cot (θ) = 25

Divide both sides by

- 7

- 7 cot (θ) = 25

Divide both sides by

- 7

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

Simplify

cot (θ) = - \frac{25}{7}

cot (θ) = - \frac{25}{7}

Verify Solutions

Find undefined (singularity) points:

cot (θ) = 0

Take the denominator(s) of

\frac{1}{cot ( θ )}

and compare to zero

cot (θ) = 0

The following points are undefined

cot (θ) = 0

Combine undefined points with solutions:

cot (θ) = - \frac{25}{7}

Apply trig inverse properties

cot (θ) = - \frac{25}{7}

General solutions for

cot (θ) = - \frac{25}{7}

cot (x) = - a \Rightarrow x = arccot (- a) + πn

θ = arccot (- \frac{25}{7}) + πn

θ = arccot (- \frac{25}{7}) + πn

Show solutions in decimal form

θ = 2.86858 \dots + πn

Popular Examples

tan(θ)=(-1)/(-2)

tan (θ) = \frac{- 1}{- 2}

sin(θ)=-1/3 ,(3pi)/2 <θ<2pi

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

4cos(x)=sqrt(5)-1

4 cos (x) = 5 - 1

2sin^2(θ)-sqrt(2)sin(θ)=0

2 sin^{2} (θ) - 2 sin (θ) = 0

sqrt(2)-cos(θ)=sqrt(2)+sin(θ)

2 - cos (θ) = 2 + sin (θ)

Frequently Asked Questions (FAQ)

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