How to solve trigonometric equation with tangent

The video tutorial explains how to solve the equation 3*tan^2(x) - 1 = 0 over the interval 0 to 2π. It begins by simplifying the equation using inverse operations, similar to algebraic methods. The tutorial then focuses on finding the values of X that satisfy the equation by using the unit circle. The instructor identifies key angles where the tangent value equals ±√3/3, specifically at π/6, 5π/6, 7π/6, and 11π/6. The lesson concludes by summarizing the solutions found within one revolution of the unit circle.

What is the first step in solving the equation 3 * tangent^2(X) - 1 = 0?

• Add 1 to both sides

• Subtract 3 from both sides

• Multiply both sides by 3

• Use inverse operations to isolate tangent^2(X)

After isolating tangent^2(X), what operation is used to solve for tangent(X)?

• Multiplication

• Square root

• Subtraction

• Addition

What is the value of tangent(X) after rationalizing the denominator?

• ± 3/sqrt(3)

• ± sqrt(3)/3

• ± 1/3

• ± sqrt(3)

Which angle in the first quadrant provides a tangent value of sqrt(3)/3?

• π/4

• π/3

• π/6

• π/2

What is the coordinate point for the angle 5π/6 on the unit circle?

• (-1/2, -sqrt(3)/2)

• (1/2, sqrt(3)/2)

• (-sqrt(3)/2, 1/2)

• (sqrt(3)/2, -1/2)

How many solutions are there for X in the interval [0, 2π]?

• Two

• Five

• Four

• Three

Which of the following is not a solution for X in the interval [0, 2π]?

• π/6

• 3π/2

• 7π/6

• 5π/6