What is the general solution for -3=1+4tan(θ) ?

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

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-3=1+4tan(θ)

- 3 = 1 + 4 tan (θ)

θ = \frac{3 π}{4} + πn

Degrees

θ = 13 5^{\circ} + 18 0^{\circ} n

Solution steps

- 3 = 1 + 4 tan (θ)

Switch sides

1 + 4 tan (θ) = - 3

Move

1

to the right side

1 + 4 tan (θ) = - 3

Subtract

1

from both sides

1 + 4 tan (θ) - 1 = - 3 - 1

Simplify

4 tan (θ) = - 4

4 tan (θ) = - 4

Divide both sides by

4

4 tan (θ) = - 4

Divide both sides by

4

\frac{4 tan ( θ )}{4} = \frac{- 4}{4}

Simplify

tan (θ) = - 1

tan (θ) = - 1

General solutions for

tan (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}

θ = \frac{3 π}{4} + πn

θ = \frac{3 π}{4} + πn

2 cos (2 θ) - 3 cos (θ) - 2 = 0

tan (2 θ) + 6 tan (θ) + 8 = 0

cos (φ) = 3 sin (φ)

5 sin (x) - 3 cos (2 x) + 3 = 0

\frac{tan ^{2} ( x )}{sec ( x ) + 1} = tan (x)

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