What is the general solution for tan(180-θ)=3sqrt(3) ?

The general solution for tan(180-θ)=3sqrt(3) is θ=180-180n-1.38067…

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Popular >

tan(180-θ)=3sqrt(3)

Solution

tan (18 0^{\circ} - θ) = 33

Solution

θ = 18 0^{\circ} - 18 0^{\circ} n - 1.38067 \dots

Radians

θ = π - 1.38067 \dots - πn

Solution steps

tan (18 0^{\circ} - θ) = 33

Apply trig inverse properties

tan (18 0^{\circ} - θ) = 33

General solutions for

tan (18 0^{\circ} - θ) = 33

tan (x) = a \Rightarrow x = arctan (a) + 18 0^{\circ} n

18 0^{\circ} - θ = arctan (33) + 18 0^{\circ} n

18 0^{\circ} - θ = arctan (33) + 18 0^{\circ} n

Solve

18 0^{\circ} - θ = arctan (33) + 18 0^{\circ} n : θ = 18 0^{\circ} - 18 0^{\circ} n - arctan (33)

18 0^{\circ} - θ = arctan (33) + 18 0^{\circ} n

Move

18 0^{\circ}

to the right side

18 0^{\circ} - θ = arctan (33) + 18 0^{\circ} n

Subtract

18 0^{\circ}

from both sides

18 0^{\circ} - θ - 18 0^{\circ} = arctan (33) + 18 0^{\circ} n - 18 0^{\circ}

Simplify

- θ = arctan (33) + 18 0^{\circ} n - 18 0^{\circ}

- θ = arctan (33) + 18 0^{\circ} n - 18 0^{\circ}

Divide both sides by

- 1

- θ = arctan (33) + 18 0^{\circ} n - 18 0^{\circ}

Divide both sides by

- 1

\frac{- θ}{- 1} = \frac{arctan ( 3 3 )}{- 1} + \frac{18 0 ^{\circ} n}{- 1} - \frac{18 0 ^{\circ}}{- 1}

Simplify

\frac{- θ}{- 1} = \frac{arctan ( 3 3 )}{- 1} + \frac{18 0 ^{\circ} n}{- 1} - \frac{18 0 ^{\circ}}{- 1}

Simplify

\frac{- θ}{- 1} : θ

\frac{- θ}{- 1}

Apply the fraction rule:

\frac{- a}{- b} = \frac{a}{b}

= \frac{θ}{1}

Apply rule

\frac{a}{1} = a

= θ

Simplify

\frac{arctan ( 3 3 )}{- 1} + \frac{18 0 ^{\circ} n}{- 1} - \frac{18 0 ^{\circ}}{- 1} : 18 0^{\circ} - 18 0^{\circ} n - arctan (33)

\frac{arctan ( 3 3 )}{- 1} + \frac{18 0 ^{\circ} n}{- 1} - \frac{18 0 ^{\circ}}{- 1}

Group like terms

= - \frac{18 0 ^{\circ}}{- 1} + \frac{18 0 ^{\circ} n}{- 1} + \frac{arctan ( 3 3 )}{- 1}

\frac{18 0 ^{\circ}}{- 1} = - 18 0^{\circ}

\frac{18 0 ^{\circ}}{- 1}

Apply the fraction rule:

\frac{a}{- b} = - \frac{a}{b}

= - 18 0^{\circ}

Apply rule

\frac{a}{1} = a

= - 18 0^{\circ}

\frac{18 0 ^{\circ} n}{- 1} = - 18 0^{\circ} n

\frac{18 0 ^{\circ} n}{- 1}

Apply the fraction rule:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{18 0 ^{\circ} n}{1}

Apply rule

\frac{a}{1} = a

= - 18 0^{\circ} n

= - (- 18 0^{\circ}) - 18 0^{\circ} n + \frac{arctan ( 3 3 )}{- 1}

Apply rule

- (- a) = a

= 18 0^{\circ} - 18 0^{\circ} n + \frac{arctan ( 3 3 )}{- 1}

\frac{arctan ( 3 3 )}{- 1} = - arctan (33)

\frac{arctan ( 3 3 )}{- 1}

Apply the fraction rule:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{arctan ( 3 3 )}{1}

Apply rule

\frac{a}{1} = a

= - arctan (33)

= 18 0^{\circ} - 18 0^{\circ} n - arctan (33)

θ = 18 0^{\circ} - 18 0^{\circ} n - arctan (33)

θ = 18 0^{\circ} - 18 0^{\circ} n - arctan (33)

θ = 18 0^{\circ} - 18 0^{\circ} n - arctan (33)

θ = 18 0^{\circ} - 18 0^{\circ} n - arctan (33)

Show solutions in decimal form

θ = 18 0^{\circ} - 18 0^{\circ} n - 1.38067 \dots

Popular Examples

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arccsc (2 x) = \frac{π}{6}

2csc(θ)=sqrt(2)cot(θ)+3csc(θ)

2 csc (θ) = 2 cot (θ) + 3 csc (θ)

sin(1/2 x)=-1

sin (\frac{1}{2} x) = - 1

9cos^2(x)tan(x)=4tan(x)

9 cos^{2} (x) tan (x) = 4 tan (x)

Frequently Asked Questions (FAQ)

What is the general solution for tan(180-θ)=3sqrt(3) ?
The general solution for tan(180-θ)=3sqrt(3) is θ=180-180n-1.38067…