What is the general solution for 1/(tan(x))=-1 ?

The general solution for 1/(tan(x))=-1 is x=(3pi)/4+pin

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Popular >

1/(tan(x))=-1

Solution

\frac{1}{tan ( x )} = - 1

Solution

x = \frac{3 π}{4} + πn

Degrees

x = 13 5^{\circ} + 18 0^{\circ} n

Solution steps

\frac{1}{tan ( x )} = - 1

Multiply both sides by

tan (x)

\frac{1}{tan ( x )} = - 1

Multiply both sides by

tan (x)

\frac{1}{tan ( x )} tan (x) = - 1 \cdot tan (x)

Simplify

1 = - tan (x)

1 = - tan (x)

Move

tan (x)

to the left side

1 = - tan (x)

Add

tan (x)

to both sides

1 + tan (x) = - tan (x) + tan (x)

Simplify

1 + tan (x) = 0

1 + tan (x) = 0

Move

1

to the right side

1 + tan (x) = 0

Subtract

1

from both sides

1 + tan (x) - 1 = 0 - 1

Simplify

tan (x) = - 1

tan (x) = - 1

Verify Solutions

Find undefined (singularity) points:

tan (x) = 0

Take the denominator(s) of

\frac{1}{tan ( x )}

and compare to zero

tan (x) = 0

The following points are undefined

tan (x) = 0

Combine undefined points with solutions:

tan (x) = - 1

General solutions for

tan (x) = - 1

tan (x)

periodicity table with

πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

x = \frac{3 π}{4} + πn

x = \frac{3 π}{4} + πn

Popular Examples

64cosh^4(x)-64cosh^2(x)-9=0

64 cosh^{4} (x) - 64 cosh^{2} (x) - 9 = 0

1+cos(θ)=1

1 + cos (θ) = 1

tan(2θ)=0.4

tan (2 θ) = 0.4

csc(θ/2)=sin(θ/2)

csc (\frac{θ}{2}) = sin (\frac{θ}{2})

sin(3x)=-1,0<= x<= 2pi

sin (3 x) = - 1, 0 \leq x \leq 2 π

Frequently Asked Questions (FAQ)

What is the general solution for 1/(tan(x))=-1 ?
The general solution for 1/(tan(x))=-1 is x=(3pi)/4+pin