Understanding Trigonometric Functions and Graphs

This video tutorial provides a comprehensive guide to graphing trigonometric functions, including sine, cosine, tangent, secant, cosecant, and cotangent. It begins with basic graphing techniques for sine and cosine, then explores transformations such as shifts and stretches. The tutorial progresses to more advanced examples, including graphing secant and cosecant using reciprocals, and concludes with techniques for graphing tangent and cotangent. The video is structured with timestamps for easy navigation.

What is the primary focus of this video tutorial?

• Graphing exponential functions

• Graphing polynomial functions

• Graphing trigonometric functions

• Graphing linear functions

Which trigonometric functions are covered in this video?

• Tangent and cotangent only

• Sine, cosine, and tangent

• Sine, cosine, tangent, secant, cosecant, and cotangent

• Sine and cosine only

What is the first step in graphing the basic sine function?

• Identify the period

• Identify the amplitude

• Shift the graph horizontally

• Plot the sine values using the unit circle

How do you determine the sine value on the unit circle?

• By looking at the x-coordinate

• By looking at the angle

• By looking at the y-coordinate

• By looking at the radius

What happens to the sine graph when the amplitude is doubled?

• The graph shifts horizontally

• The graph remains unchanged

• The graph compresses vertically

• The graph stretches vertically

What is the effect of a negative sign in front of the cosine function?

• It stretches the graph vertically

• It reflects the graph over the x-axis

• It compresses the graph horizontally

• It shifts the graph up

How is the secant function related to the cosine function?

• Secant is the integral of cosine

• Secant is the reciprocal of cosine

• Secant is the inverse of cosine

• Secant is the derivative of cosine

What is the period of the basic tangent function?

• 2π

• π

• 4π

• π/2

What is the effect of a coefficient greater than 1 in front of the tangent function?

• It shifts the graph horizontally

• It reflects the graph over the y-axis

• It compresses the graph vertically

• It stretches the graph vertically

How does the graph of cotangent differ from tangent?

• Cotangent graph goes up to the right

• Cotangent graph goes down to the right

• Cotangent graph is a horizontal line

• Cotangent graph is a vertical line