Trigonometric Equations and Functions

The video tutorial explains how to solve the trigonometric equation 3 tangent squared X - 1 = 0 within the interval from 0 to 2π. It begins by isolating tangent squared X and solving for tangent X using square roots. The tutorial then uses 30-60-90 triangles to find reference angles and express solutions in both degrees and radians. It concludes by discussing alternative methods like using the unit circle.

What is the first step in solving the equation 3 tangent squared x - 1 = 0?

• Divide both sides by 3

• Multiply both sides by 3

• Add 1 to both sides

• Subtract 1 from both sides

After isolating tangent squared x, what operation is performed to solve for tangent x?

• Square both sides

• Cube both sides

• Take the square root of both sides

• Take the cube root of both sides

Which triangle is used to determine where tangent x equals ±1/√3?

• Equilateral triangle

• Isosceles triangle

• 30-60-90 triangle

• 45-45-90 triangle

What is the reference angle in degrees for tangent x = ±1/√3?

• 30 degrees

• 60 degrees

• 45 degrees

• 90 degrees

In which quadrants is the reference angle sketched to find all solutions?

• All four quadrants

• First and third quadrants

• First and second quadrants

• Second and fourth quadrants

What is the radian measure equivalent to 30 degrees?

• π/4

• π/3

• π/6

• π/2

Which of the following is a solution in radians for the equation on the given interval?

• 2π/3

• π/2

• 5π/6

• 3π/4

What is the radian measure for 330 degrees?

• 11π/6

• 5π/3

• 7π/6

• 2π

Why might using the unit circle be more challenging for tangent compared to sine or cosine?

• Tangent is always positive

• Tangent is not defined on the unit circle

• Tangent requires calculating quotients of fractions

• Tangent involves division by zero

What is important to be familiar with when solving trigonometric equations?

• Unit circles

• Complex numbers

• Graphing calculators

• Reference triangles