What is the general solution for tan(2x-60)=3sqrt(3) ?

The general solution for tan(2x-60)=3sqrt(3) is x=30+(pin)/2+(1.38067…)/2

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tan(2x-60)=3sqrt(3)

tan (2 x - 60) = 33

x = 30 + \frac{πn}{2} + \frac{1.38067 \dots}{2}

Degrees

x = 1758.42668 \dots^{\circ} + 9 0^{\circ} n

Solution steps

tan (2 x - 60) = 33

Apply trig inverse properties

tan (2 x - 60) = 33

General solutions for

tan (2 x - 60) = 33

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

2 x - 60 = arctan (33) + πn

2 x - 60 = arctan (33) + πn

Solve

2 x - 60 = arctan (33) + πn : x = 30 + \frac{πn}{2} + \frac{arctan ( 3 3 )}{2}

2 x - 60 = arctan (33) + πn

Move

60

to the right side

2 x - 60 = arctan (33) + πn

Add

60

to both sides

2 x - 60 + 60 = arctan (33) + πn + 60

Simplify

2 x = arctan (33) + πn + 60

2 x = arctan (33) + πn + 60

Divide both sides by

2

2 x = arctan (33) + πn + 60

Divide both sides by

2

\frac{2 x}{2} = \frac{arctan ( 3 3 )}{2} + \frac{πn}{2} + \frac{60}{2}

Simplify

\frac{2 x}{2} = \frac{arctan ( 3 3 )}{2} + \frac{πn}{2} + \frac{60}{2}

Simplify

\frac{2 x}{2} : x

\frac{2 x}{2}

Divide the numbers:

\frac{2}{2} = 1

= x

Simplify

\frac{arctan ( 3 3 )}{2} + \frac{πn}{2} + \frac{60}{2} : 30 + \frac{πn}{2} + \frac{arctan ( 3 3 )}{2}

\frac{arctan ( 3 3 )}{2} + \frac{πn}{2} + \frac{60}{2}

Group like terms

= \frac{60}{2} + \frac{πn}{2} + \frac{arctan ( 3 3 )}{2}

Divide the numbers:

\frac{60}{2} = 30

= 30 + \frac{πn}{2} + \frac{arctan ( 3 3 )}{2}

x = 30 + \frac{πn}{2} + \frac{arctan ( 3 3 )}{2}

x = 30 + \frac{πn}{2} + \frac{arctan ( 3 3 )}{2}

x = 30 + \frac{πn}{2} + \frac{arctan ( 3 3 )}{2}

x = 30 + \frac{πn}{2} + \frac{arctan ( 3 3 )}{2}

Show solutions in decimal form

x = 30 + \frac{πn}{2} + \frac{1.38067 \dots}{2}

sin (x) = \frac{0.46}{9.46}

2 cos^{2} (x) - 7 cos (x) + 3 = 0, 0 < x < 2 π

arccos (x) = arcsin (\frac{1}{3}) + arcsin (\frac{7}{9})

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

tan (θ) = - \frac{1}{5}

What is the general solution for tan(2x-60)=3sqrt(3) ?
The general solution for tan(2x-60)=3sqrt(3) is x=30+(pin)/2+(1.38067…)/2