Trigonometric Functions and Their Properties

The video tutorial reviews trigonometric functions and their reciprocals, explaining the origins of their names. It then explores how to modify trigonometric graphs, focusing on changes in frequency and period. The tutorial provides a detailed explanation of how these modifications affect the appearance and behavior of the graphs, using sine as an example.

What is the reciprocal of the sine function called?

• Secant

• Cotangent

• Cosecant

• Tangent

Why is the cosine function named as such?

• It is a complement to sine

• It is a historical term

• It represents a wave

• It is derived from tangent

What does the 'co' in cosine stand for?

• Curve

• Coordinate

• Complement

• Constant

How can the appearance of a sine graph be changed?

• By adding a constant

• By rotating the graph

• By multiplying the angle

• By changing the axis

What happens to the sine graph when the angle is multiplied by 2?

• The graph shifts

• The graph compresses

• The graph remains unchanged

• The graph stretches

What is the effect of multiplying the angle in a sine function by a number greater than 1?

• Decreases the amplitude

• Increases the amplitude

• Decreases the period

• Increases the period

What term describes the number of complete cycles a graph makes in a given interval?

• Amplitude

• Period

• Frequency

• Phase

If the period of a sine graph is halved, what happens to its frequency?

• It quadruples

• It halves

• It doubles

• It remains the same

What is the period of a sine function when the angle is divided by 2?

• 180 degrees

• 360 degrees

• 720 degrees

• 90 degrees

How is the period of a trigonometric function calculated when the angle is multiplied by a constant?

• 360 multiplied by the constant

• 180 multiplied by the constant

• 360 divided by the constant

• 180 divided by the constant