Understanding Trigonometric Functions and Their Graphs

The video tutorial redefines trigonometric functions using the unit circle, explaining how sine, cosine, and tangent relate to the circle's coordinates. It then focuses on graphing the sine function, demonstrating how its values change as the angle varies. The tutorial concludes by exploring the sine wave's oscillatory nature and its continuous pattern across the theta axis.

What is the y-coordinate of a point on the unit circle used to define?

• Cosine of theta

• Radius of the circle

• Sine of theta

• Tangent of theta

How is the tangent of an angle defined in terms of sine and cosine?

• Cosine minus sine

• Sine divided by cosine

• Cosine divided by sine

• Sine multiplied by cosine

What is the sine of theta when theta is 0 radians?

• Undefined

• 0

• -1

• 1

At which point does the radius intersect the unit circle when theta is pi radians?

• (0, -1)

• (0, 1)

• (-1, 0)

• (1, 0)

What is the sine of theta when theta is 3pi/2 radians?

• 1

• 0

• -1

• Undefined

What is the shape of the graph of the sine function?

• Exponential

• Sine wave

• Parabolic

• Linear

What is the maximum value that the sine function can reach?

• -1

• 0

• 1

• 2

How does the sine wave behave for negative values of theta?

• It stops

• It mirrors the positive side

• It continues oscillating

• It becomes a straight line

What is the range of the sine function?

• 0 to infinity

• 0 to 1

• -1 to 1

• -2 to 2

What will be covered in the next module?

• Graph of the cosine function

• Graph of the secant function

• Graph of the tangent function

• Graph of the cotangent function