Trigonometric Functions and Their Properties

The video tutorial explains how to solve the trigonometric equation 2 sin(θ) - √2 = 0 within a given interval. It demonstrates two methods: using the unit circle and reference triangles. The unit circle method involves identifying angles where the sine value is √2/2, specifically at 45° (π/4 radians) and 135° (3π/4 radians). The reference triangle method uses 45-45-90 triangles to confirm these solutions. The tutorial emphasizes understanding both methods for solving trigonometric equations.

What is the first step in solving the equation 2 sin(θ) - √2 = 0?

• Divide both sides by 2

• Add √2 to both sides

• Subtract √2 from both sides

• Multiply both sides by 2

In which quadrants must the solutions be found for sin(θ) = √2/2?

• First and third quadrants

• Third and fourth quadrants

• First and second quadrants

• Second and fourth quadrants

What is the angle in radians where sin(θ) = √2/2 in the first quadrant?

• π/2

• π/3

• π/4

• π/6

Which angle corresponds to sin(θ) = √2/2 in the second quadrant?

• 3π/4

• 2π/3

• π/3

• 5π/6

What is the sine value of a 45-degree angle?

• √2/2

• √3/2

• 1

• 1/2

Which method involves using the y-coordinate on a circle?

• Unit circle method

• Algebraic method

• Reference triangle method

• Graphical method

What type of triangle is used as a reference for sin(θ) = √2/2?

• 30-30-120 triangle

• 60-60-60 triangle

• 45-45-90 triangle

• 30-60-90 triangle

What is the ratio of the opposite side to the hypotenuse in a 45-45-90 triangle?

• 1/2

• √2/2

• √3/2

• 1/√2

What is the significance of rationalizing the denominator in trigonometry?

• It is unnecessary

• It alters the quadrant

• It changes the angle

• It simplifies the expression

Why is it important to understand both the unit circle and reference triangle methods?

• To memorize all trigonometric values

• To solve equations not recognized on the unit circle

• Because they are the only methods available

• To avoid using calculators