What is the general solution for 7tan(θ)=3sqrt(3)+tan(θ) ?

The general solution for 7tan(θ)=3sqrt(3)+tan(θ) is θ=0.71372…+pin

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7tan(θ)=3sqrt(3)+tan(θ)

7 tan (θ) = 33 + tan (θ)

θ = 0.71372 \dots + πn

Degrees

θ = 40.89339 \dots^{\circ} + 18 0^{\circ} n

Solution steps

7 tan (θ) = 33 + tan (θ)

Solve by substitution

7 tan (θ) = 33 + tan (θ)

Let:

tan (θ) = u

7 u = 33 + u

7 u = 33 + u : u = \frac{3}{2}

7 u = 33 + u

Move

u

to the left side

7 u = 33 + u

Subtract

u

from both sides

7 u - u = 33 + u - u

Simplify

6 u = 33

6 u = 33

Divide both sides by

6

6 u = 33

Divide both sides by

6

\frac{6 u}{6} = \frac{3 3}{6}

Simplify

u = \frac{3}{2}

u = \frac{3}{2}

Substitute back

u = tan (θ)

tan (θ) = \frac{3}{2}

tan (θ) = \frac{3}{2}

tan (θ) = \frac{3}{2} : θ = arctan (\frac{3}{2}) + πn

tan (θ) = \frac{3}{2}

Apply trig inverse properties

tan (θ) = \frac{3}{2}

General solutions for

tan (θ) = \frac{3}{2}

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

θ = arctan (\frac{3}{2}) + πn

θ = arctan (\frac{3}{2}) + πn

Combine all the solutions

θ = arctan (\frac{3}{2}) + πn

Show solutions in decimal form

θ = 0.71372 \dots + πn

sin (3 x) - sin (x) = 0

2 sin (x) - 4 cos (x) = 3, 0 \leq x \leq 2 π

sec^{2} (θ) - 6 sec (θ) + 8 = 0

sin^{2} (x) - cos^{2} (x) - sin (x) = 0

10 tan (x) sin (x) = sin (x)

What is the general solution for 7tan(θ)=3sqrt(3)+tan(θ) ?
The general solution for 7tan(θ)=3sqrt(3)+tan(θ) is θ=0.71372…+pin