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Chapter 5: Problem 41

Solve the multiple-angle equation. $$\tan 3 x-1=0$$

Short Answer

Expert verified
\( x = \pi/12 + n \pi/3 \)

Step by step solution

01

Rewrite the equation

First of all, we need to rewrite our equation to express it in the form where we can determine the angle for the tangent. Our equation becomes: \( \tan(3x) = 1 \)
02

Find the angle of tangent

Next, we need to find the angle corresponding to the tangent, knowing that the tangent of an angle of \( \pi/4 \) or \( 45^{\circ} \) is 1. Thus we get \( 3x = \pi/4 + n \pi \), where \( n \) is an integer encompassing all possible solutions for tangent.
03

Solve for x

Finally, we solve for x in our equation, dividing the whole equation by 3, so \( x = \pi/12 + n \pi/3 \).

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