Trigonometric Functions and Their Properties

The video tutorial covers various trigonometric concepts using the unit circle. It begins with identifying points on the unit circle for specific angles, such as pi/3, and determining angles with positive cosine values. The tutorial then explores finding angles where the sine equals 0.4 and where the cosine is zero. It also discusses reflections of angles on the unit circle and identifies quadrants where the x-coordinate is greater than the y-coordinate. Finally, the video explains graph translation of functions, specifically how a function is translated when modified by a constant.

Which point on the unit circle corresponds to the cosine of pi over 3?

• A

• B

• C

• D

In which quadrant is the cosine value positive?

• First and Second

• Third and Fourth

• First and Fourth

• Second and Third

What is the cosine value of an angle in the first quadrant?

• Positive

• Negative

• Zero

• Undefined

Which angle has a positive cosine value?

• 7 pi over 6

• 5 pi over 3

• 3 pi over 4

• 5 pi over 6

What is the sine value of an angle with a y-coordinate of 0.4 on the unit circle?

• 1.0

• 0.8

• 0.6

• 0.4

How many angles on the unit circle have a sine value of 0.4?

• One

• Two

• Three

• Four

At which angle is the cosine value zero?

• Pi/2

• 2 Pi

• 3 Pi/2

• Pi

What is the sine value at theta = 3 pi/2?

• 0.5

• -1

• 1

• 0

Which angle is a reflection over the y-axis?

• 7 Pi/4

• Pi/4

• 5 Pi/4

• 3 Pi/4

What are the coordinates of an angle in the second quadrant?

• Negative x, Negative y

• Negative x, Positive y

• Positive x, Negative y

• Positive x, Positive y