What is the general solution for tan(2θ)=(-81)/(81) ?

The general solution for tan(2θ)=(-81)/(81) is θ=(3pi)/8+(pin)/2

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tan(2θ)=(-81)/(81)

tan (2 θ) = \frac{- 81}{81}

θ = \frac{3 π}{8} + \frac{πn}{2}

Radians

θ = \frac{3 π}{8} + \frac{π}{2} n

Solution steps

tan (2 θ) = \frac{- 81}{81}

Simplify

\frac{- 81}{81} : - 1

\frac{- 81}{81}

Apply the fraction rule:

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

= - \frac{81}{81}

Apply rule

\frac{a}{a} = 1

= - 1

General solutions for

tan (2 θ) = - 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}

2 θ = \frac{3 π}{4} + πn

2 θ = \frac{3 π}{4} + πn

Solve

2 θ = \frac{3 π}{4} + πn : θ = \frac{3 π}{8} + \frac{πn}{2}

2 θ = \frac{3 π}{4} + πn

Divide both sides by

2

2 θ = \frac{3 π}{4} + πn

Divide both sides by

2

\frac{2 θ}{2} = \frac{\frac{3 π}{4}}{2} + \frac{πn}{2}

Simplify

\frac{2 θ}{2} = \frac{\frac{3 π}{4}}{2} + \frac{πn}{2}

Simplify

\frac{2 θ}{2} : θ

\frac{2 θ}{2}

Divide the numbers:

\frac{2}{2} = 1

= θ

Simplify

\frac{\frac{3 π}{4}}{2} + \frac{πn}{2} : \frac{3 π}{8} + \frac{πn}{2}

\frac{\frac{3 π}{4}}{2} + \frac{πn}{2}

\frac{\frac{3 π}{4}}{2} = \frac{3 π}{8}

\frac{\frac{3 π}{4}}{2}

Apply the fraction rule:

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

= \frac{3 π}{4 \cdot 2}

Multiply the numbers:

4 \cdot 2 = 8

= \frac{3 π}{8}

= \frac{3 π}{8} + \frac{πn}{2}

θ = \frac{3 π}{8} + \frac{πn}{2}

θ = \frac{3 π}{8} + \frac{πn}{2}

θ = \frac{3 π}{8} + \frac{πn}{2}

θ = \frac{3 π}{8} + \frac{πn}{2}

sin (θ) cos (2 θ) - cos (2 θ) = 0

tan (θ) = - \frac{7}{6}

8 sin^{2} (x) - 1 = 5

sin (d) = 0.8

csc (θ) = \frac{17}{8}

What is the general solution for tan(2θ)=(-81)/(81) ?
The general solution for tan(2θ)=(-81)/(81) is θ=(3pi)/8+(pin)/2