How to find all of the solutions of an equation with the triple angle of tangent

The video tutorial explains how to solve a trigonometric problem involving tangent and the unit circle. It begins by identifying the first solution where the tangent of an angle equals one, using the unit circle. The tutorial then explores additional solutions and generalizes the solution for all real numbers. Finally, it demonstrates how to find solutions within a specific range, such as between 0 and 2π, by substituting different values into the general solution formula.

What is the tangent of an angle in terms of the unit circle?

• The difference between the x and y coordinates

• The sum of the x and y coordinates

• The ratio of the y-coordinate to the x-coordinate

• The ratio of the x-coordinate to the y-coordinate

Which angle in the first quadrant has a tangent of 1?

• π/3

• π/4

• π/6

• π/2

How can additional solutions for the tangent equation be found?

• By dividing the initial solution by 2

• By subtracting π from the initial solution

• By adding π to the initial solution

• By multiplying the initial solution by 2

What is the simplified expression for all solutions of the tangent equation?

• 3X = π/4 + 2πN

• 3X = π/4 + πN

• 3X = π/2 + πN

• 3X = π/6 + πN

How do you find solutions for the tangent equation between 0 and 2π?

• By using only negative values of n

• By substituting different values for n and checking the range

• By setting n to zero

• By using only positive values of n