Trigonometric Functions and Their Properties

The video tutorial covers the graphing of trigonometric functions, focusing on sine, cosecant, tangent, and their periods. It explains how to use the unit circle to understand tangent's period and compares the periods of various trigonometric functions. The tutorial also demonstrates graphing techniques, including shifting and identifying asymptotes, and applies these concepts to real-world scenarios. The video concludes with a summary of key takeaways.

How can the graph of sine be used to graph cosecant?

• By reflecting the sine graph over the x-axis

• By drawing parabolas at the maximum and minimum points of the sine graph

• By shifting the sine graph horizontally

• By inverting the sine graph

What is the period of the tangent function?

• π/2

• π

• 4π

• 2π

Which trigonometric functions have the same period as their inverses?

• All of the above

• Cosine and Secant

• Tangent and Cotangent

• Sine and Cosecant

How do you determine the horizontal shift of a trigonometric function?

• By looking at the coefficient of x

• By examining the constant added to x

• By finding the amplitude

• By calculating the period

How is the period of a trigonometric function affected by a coefficient in front of x?

• The period is multiplied by the coefficient

• The period is divided by the coefficient

• The period is added to the coefficient

• The period is subtracted from the coefficient

What is the symmetry property of tangent?

• Tangent is neither even nor odd

• Tangent is both even and odd

• Tangent is an odd function

• Tangent is an even function

How does the symmetry property affect the graph of sine?

• Sine is both even and odd, so it is symmetric about both axes

• Sine is neither even nor odd, so it has no symmetry

• Sine is an odd function, so it is symmetric about the origin

• Sine is an even function, so it is symmetric about the y-axis

What is the domain of the function representing the distance from a fisherman to a boat?

• -π to π

• 0 to 2π

• -π/2 to π/2

• 0 to π

What happens to the height of a rocket as the angle of elevation approaches 60 seconds?

• The height decreases

• The height remains constant

• The height approaches infinity

• The height approaches zero

What is the minimum distance between the fisherman and the boat?

• 2 kilometers

• 1.5 kilometers

• 0.5 kilometers

• 3 kilometers