Trigonometric Functions and Identities

This video provides a comprehensive review of Unit 3 for AP Precalculus, covering trigonometric and polar functions. It explains the properties and graphing of sine, cosine, and tangent functions, including transformations and inverse functions. The video also discusses solving trigonometric equations and using trigonometric identities. Finally, it introduces polar coordinates and graphing polar functions, offering insights into different types of polar graphs.

What is the radian measure of an angle whose arc length is equal to the radius of the circle?

• 1 radian

• 2π radians

• 0 radians

• π radians

In the unit circle, what is the sine of an angle θ?

• The radius of the circle

• The y-coordinate of the point

• The angle in degrees

• The x-coordinate of the point

Which of the following describes the amplitude of a sine or cosine function?

• The distance from the midline to the maximum or minimum value

• The vertical shift of the graph

• The horizontal shift of the graph

• The period of the function

How does a negative 'a' value affect the graph of a sine or cosine function?

• It shifts the graph to the right

• It reflects the graph across the x-axis

• It increases the period of the graph

• It decreases the amplitude of the graph

What is the range of angles for the inverse sine function to ensure it remains a function?

• -π/2 to π/2

• -π to π

• 0 to π

• 0 to 2π

What is the correct co-terminal angle for a tangent value of -1 within the restricted range?

• 5π/6

• π/3

• -π/4

• 7π/4

Which identity is used to express tangent in terms of sine and cosine?

• Pythagorean Identity

• Double Angle Identity

• Reciprocal Identity

• Quotient Identity

What is the main purpose of trigonometric identities in solving equations?

• To convert angles to radians

• To simplify or rewrite trigonometric functions

• To find the exact value of angles

• To determine the quadrant of an angle

In polar coordinates, what does the first value in the pair (r, θ) represent?

• The angle in degrees

• The x-coordinate

• The radius

• The y-coordinate

How many petals does a rose curve have if n is even and equals 4?

• 8 petals

• 12 petals

• 16 petals

• 4 petals