What is the general solution for 3tan(1/3 x)=8 ?

The general solution for 3tan(1/3 x)=8 is x=3*1.21202…+3pin

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3tan(1/3 x)=8

3 tan (\frac{1}{3} x) = 8

x = 3 \cdot 1.21202 \dots + 3 πn

Degrees

x = 208.33186 \dots^{\circ} + 54 0^{\circ} n

Solution steps

3 tan (\frac{1}{3} x) = 8

Divide both sides by

3

3 tan (\frac{1}{3} x) = 8

Divide both sides by

3

\frac{3 tan ( \frac{1}{3} x )}{3} = \frac{8}{3}

Simplify

tan (\frac{1}{3} x) = \frac{8}{3}

tan (\frac{1}{3} x) = \frac{8}{3}

Apply trig inverse properties

tan (\frac{1}{3} x) = \frac{8}{3}

General solutions for

tan (\frac{1}{3} x) = \frac{8}{3}

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

\frac{1}{3} x = arctan (\frac{8}{3}) + πn

\frac{1}{3} x = arctan (\frac{8}{3}) + πn

Solve

\frac{1}{3} x = arctan (\frac{8}{3}) + πn : x = 3 arctan (\frac{8}{3}) + 3 πn

\frac{1}{3} x = arctan (\frac{8}{3}) + πn

Multiply both sides by

3

\frac{1}{3} x = arctan (\frac{8}{3}) + πn

Multiply both sides by

3

3 \cdot \frac{1}{3} x = 3 arctan (\frac{8}{3}) + 3 πn

Simplify

x = 3 arctan (\frac{8}{3}) + 3 πn

x = 3 arctan (\frac{8}{3}) + 3 πn

x = 3 arctan (\frac{8}{3}) + 3 πn

Show solutions in decimal form

x = 3 \cdot 1.21202 \dots + 3 πn

1.6 5^{2} = 0.6 5^{2} + 1.7 7^{2} - 2 (0.65) (1.77) cos (A)

x, cos (3 x + \frac{π}{4}) = \frac{1}{2}

0 = 2 - 3 \cdot sin (x) - (cos^{2} (x) - sin^{2} (x))

x, cos^{2} (3 x + \frac{π}{4}) = \frac{3}{4}

\frac{tan ( x ^{2} + 6 ) - 1}{tan ( x )} = 0

What is the general solution for 3tan(1/3 x)=8 ?
The general solution for 3tan(1/3 x)=8 is x=3*1.21202…+3pin