What is the general solution for tan(bx)=5 ?

The general solution for tan(bx)=5 is x=(1.37340…)/b+(pin)/b

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tan(bx)=5

tan (b x) = 5

x = \frac{1.37340 \dots}{b} + \frac{πn}{b}

Solution steps

tan (b x) = 5

Apply trig inverse properties

tan (b x) = 5

General solutions for

tan (b x) = 5

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

b x = arctan (5) + πn

b x = arctan (5) + πn

Solve

b x = arctan (5) + πn : x = \frac{arctan ( 5 )}{b} + \frac{πn}{b}; b \neq = 0

b x = arctan (5) + πn

Divide both sides by

b; b \neq = 0

b x = arctan (5) + πn

Divide both sides by

b; b \neq = 0

\frac{b x}{b} = \frac{arctan ( 5 )}{b} + \frac{πn}{b}; b \neq = 0

Simplify

x = \frac{arctan ( 5 )}{b} + \frac{πn}{b}; b \neq = 0

x = \frac{arctan ( 5 )}{b} + \frac{πn}{b}; b \neq = 0

x = \frac{arctan ( 5 )}{b} + \frac{πn}{b}

Show solutions in decimal form

x = \frac{1.37340 \dots}{b} + \frac{πn}{b}

What is the general solution for tan(bx)=5 ?
The general solution for tan(bx)=5 is x=(1.37340…)/b+(pin)/b