Solving an equation with tangent with no restrictions

The video tutorial explains how to solve a tangent equation, initially within the interval of 0 to 2π, and then extends the solution to include all possible angles by removing the interval restriction. It covers the concept of tangent on the unit circle, the periodic nature of the tangent function, and how to express solutions in a general form using π. The tutorial emphasizes understanding the infinite nature of solutions when constraints are removed.

What is the first step in solving the equation 3 * tan(x) + 3 = 0?

• Subtract 3 from both sides

• Multiply both sides by 3

• Divide both sides by 3

• Add 3 to both sides

Which angles within the interval [0, 2π] make tan(x) equal to -1?

• π/2 and 3π/2

• π/4 and 5π/4

• 0 and π

• 3π/4 and 7π/4

What is the significance of the unit circle in this context?

• It is used to solve linear equations

• It provides only one solution

• It restricts solutions to positive angles

• It helps find angles where tan(x) = -1

What is the periodicity of the tangent function?

• 2π

• π

• π/2

• 4π

What does removing the interval restriction allow us to do?

• Find only one solution

• Consider solutions beyond 2π

• Ignore the unit circle

• Use only positive angles

How can the general solution for tan(x) = -1 be expressed?

• 3π/4 + 2πn

• π/4 + πn

• 7π/4 + πn

• 3π/4 + πn

Why is it unnecessary to write both 3π/4 + πn and 7π/4 + πn?

• They are the same angle

• They are not solutions

• One is a multiple of the other

• Adding π covers both solutions