Trigonometric Functions and Unit Circle

The video tutorial explains how to solve the equation S of 2x equals 3/2 by using the unit circle. It begins with an introduction to the problem and the concept of the unit circle, followed by identifying angles where the sine of an angle equals -3/2. The tutorial then demonstrates how to find all solutions by adding co-terminal angles and concludes with deriving the final solution.

What is the first step in solving the equation S of 2x equals 3 divided by 2?

• Find the cosine of the angle

• Determine the tangent of the angle

• Find solutions within the interval 0 to 2π

• Calculate the secant of the angle

Why is it important to find solutions within the interval 0 to 2π first?

• To simplify the equation

• To ensure all possible solutions are found

• To limit the number of solutions

• To convert angles to degrees

What does the sine of an angle represent on the unit circle?

• The angle in degrees

• The x-coordinate of the point

• The y-coordinate of the point

• The radius of the circle

What is the purpose of creating a unit circle in this context?

• To calculate the area of the circle

• To determine the sine and cosine values

• To find the radius of the circle

• To measure angles in degrees

What is the relationship between the sine of an angle and the y-coordinate on the unit circle?

• They are unrelated

• The sine is half the y-coordinate

• The sine is double the y-coordinate

• They are equal

Which angles on the unit circle have a sine value of 3/2?

• π/4 and 3π/4

• π/6 and 5π/6

• 4π/3 and 5π/3

• π/2 and 3π/2

What is the first angle identified where the sine equals 3/2?

• π/3

• 5π/3

• π/2

• 4π/3

What is the second angle identified where the sine equals 3/2?

• π/2

• 5π/3

• 4π/3

• π/3

What is the significance of co-terminal angles in finding all solutions?

• They only apply to cosine functions

• They are irrelevant to the solution

• They allow for finding solutions beyond the initial interval

• They limit the solutions to a single interval

How do you find additional solutions beyond the interval 0 to 2π?

• By subtracting π

• By adding 2π repeatedly

• By multiplying by 2

• By dividing by 2