What is the general solution for -3tan(θ)-11=3tan(θ)-6 ?

The general solution for -3tan(θ)-11=3tan(θ)-6 is θ=-0.69473…+pin

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

-3tan(θ)-11=3tan(θ)-6

- 3 tan (θ) - 11 = 3 tan (θ) - 6

θ = - 0.69473 \dots + πn

Degrees

θ = - 39.80557 \dots^{\circ} + 18 0^{\circ} n

Solution steps

- 3 tan (θ) - 11 = 3 tan (θ) - 6

Solve by substitution

- 3 tan (θ) - 11 = 3 tan (θ) - 6

Let:

tan (θ) = u

- 3 u - 11 = 3 u - 6

- 3 u - 11 = 3 u - 6 : u = - \frac{5}{6}

- 3 u - 11 = 3 u - 6

Move

11

to the right side

- 3 u - 11 = 3 u - 6

Add

11

to both sides

- 3 u - 11 + 11 = 3 u - 6 + 11

Simplify

- 3 u = 3 u + 5

- 3 u = 3 u + 5

Move

3 u

to the left side

- 3 u = 3 u + 5

Subtract

3 u

from both sides

- 3 u - 3 u = 3 u + 5 - 3 u

Simplify

- 6 u = 5

- 6 u = 5

Divide both sides by

- 6

- 6 u = 5

Divide both sides by

- 6

\frac{- 6 u}{- 6} = \frac{5}{- 6}

Simplify

u = - \frac{5}{6}

u = - \frac{5}{6}

Substitute back

u = tan (θ)

tan (θ) = - \frac{5}{6}

tan (θ) = - \frac{5}{6}

tan (θ) = - \frac{5}{6} : θ = arctan (- \frac{5}{6}) + πn

tan (θ) = - \frac{5}{6}

Apply trig inverse properties

tan (θ) = - \frac{5}{6}

General solutions for

tan (θ) = - \frac{5}{6}

tan (x) = - a \Rightarrow x = arctan (- a) + πn

θ = arctan (- \frac{5}{6}) + πn

θ = arctan (- \frac{5}{6}) + πn

Combine all the solutions

θ = arctan (- \frac{5}{6}) + πn

Show solutions in decimal form

θ = - 0.69473 \dots + πn

cos^{2} (x) - 6 cos (x) - 1 = 0

tan (5 x) tan (x) = tan (5 x)

4 sin^{2} (x) = 1 + 4 cos (x)

4 sec (θ) + 23 = sec (θ)

2 cos (3 x) - 3 = 0

What is the general solution for -3tan(θ)-11=3tan(θ)-6 ?
The general solution for -3tan(θ)-11=3tan(θ)-6 is θ=-0.69473…+pin