Understanding Reference Angles and Positive Angles

The video tutorial explains how to find the reference angle and the smallest positive angle for a point on the terminal side of an angle. It begins by sketching the angle in standard position and forming a reference triangle. The sides of the triangle are labeled using the coordinates of the point. The reference angle is calculated using the tangent function, and the smallest positive angle is determined by adding the reference angle to pi, as the point lies in the third quadrant. The tutorial concludes with a summary of the findings.

What is the initial step in finding the reference angle for a point on the terminal side of an angle?

• Finding the hypotenuse of the triangle

• Calculating the tangent of the angle

• Identifying the coordinates of the point

• Sketching the reference triangle

In which direction do we rotate to sketch the smallest positive angle in standard position?

• Horizontally

• Counterclockwise

• Vertically

• Clockwise

What is the reference angle in a right triangle formed by a point on the terminal side?

• The angle between the positive x-axis and the terminal side

• The angle between the y-axis and the terminal side

• The angle between the hypotenuse and the terminal side

• The angle between the negative x-axis and the terminal side

How do you label the sides of the reference triangle when determining the reference angle?

• Using the product of x and y

• Using the absolute values of x and y

• Using the sum of x and y

• Using the original negative values of x and y

What is the value of tangent theta when the opposite side is 6 and the adjacent side is 3?

• 2

• 3

• 1

• 0.5

What is the approximate value of the reference angle in radians?

• 0.7854

• 1.1071

• 1.5708

• 2.3562

Why do we use positive values for x and y when determining the reference angle?

• Because the reference angle is always reflex

• Because the reference angle is always right

• Because the reference angle is always acute

• Because the reference angle is always obtuse

What is the formula to find the smallest positive angle containing the given point?

• 2pi - reference angle

• 2pi + reference angle

• pi + reference angle

• pi - reference angle

What is the approximate value of the smallest positive angle in radians?

• 3.1416

• 4.2487

• 5.4978

• 6.2832

In which quadrant does the smallest positive angle terminate?

• First quadrant

• Second quadrant

• Fourth quadrant

• Third quadrant