Understanding Sine and the Unit Circle

The video tutorial explores solving the equation sine of X equals 1/3 by using the unit circle and inverse sine function. It begins with a problem statement, followed by a review of the unit circle and sine function. The tutorial then calculates specific X values using inverse sine and formulates a solution set by adding multiples of 2π. The solution set is verified by checking which values satisfy the original equation.

What is the main goal of the problem presented in the video?

• To solve for X in a quadratic equation

• To determine the tangent of X

• To calculate the cosine of X

• To find the X values where sine of X equals 1/3

What is the radius of the unit circle?

• π

• 1

• 0.5

• 2

In which quadrants does the inverse sine function provide values?

• Third and fourth

• Second and third

• First and fourth

• First and second

What is the approximate value of the angle where sine equals 1/3, rounded to the nearest hundredth?

• 3.14 radians

• 2.80 radians

• 1.57 radians

• 0.34 radians

What is the range of the inverse sine function?

• 0 to 2π

• -π/2 to π/2

• -π to π

• 0 to π

Which of the following is part of the solution set for sine of X equals 1/3?

• 2.8 + πN

• Negative 0.34 + 2πN

• 2.8 + 2πN

• 0.34 + πN

What happens if you add π to the angle 0.34?

• You get an angle with sine equal to 1/3

• You get an angle with sine equal to -1/3

• You get an angle with sine equal to 0

• You get an angle with sine equal to 1

What is the significance of adding multiples of 2π to an angle?

• It returns to the same point on the unit circle

• It results in a different angle

• It doubles the angle

• It changes the sine value

Which angle, when added to 2πN, is part of the solution set?

• 0.34

• 1.57

• 3.14

• Negative 0.34

What is the result of subtracting 0.34 from π?

• 2.80 radians

• 0.34 radians

• 3.14 radians

• 1.57 radians