Understanding Sine Function Properties

The video tutorial explains the origin of the sine function by using a circle with a radius of 12 inches and inscribed right triangles. It demonstrates how the sine function is derived from the ratio of the height of these triangles to the circle's radius. The tutorial calculates sine values for angles of 30, 45, 60, and 90 degrees, and explains the transition to negative values beyond 180 degrees. The session concludes with a preview of the next tutorial, which will discuss the utility of the sine function.

What is the primary purpose of plotting the sine function in terms of degrees?

• To make it easier to understand the function's origin

• To complicate the understanding of the function

• To avoid using radians

• To focus on the x-axis only

What is the radius of the circle used to inscribe the triangles?

• 12 inches

• 15 inches

• 20 inches

• 10 inches

How is the sine function derived from the inscribed triangles?

• By dividing the base of the triangle by the hypotenuse

• By dividing the height of the triangle by the hypotenuse

• By dividing the hypotenuse by the base

• By dividing the hypotenuse by the height

What is the sine value for a 30-degree angle?

• 0.8

• 1.0

• 0.7

• 0.5

What is the sine value for a 45-degree angle?

• 1.0

• 0.5

• 0.707

• 0.866

What is the sine value for a 60-degree angle?

• 0.5

• 0.707

• 0.866

• 1.0

What happens to the sine value at 90 degrees?

• It becomes zero

• It is undefined

• It becomes negative

• It equals the radius divided by the radius

What is the sine value for a 210-degree angle?

• -0.707

• 0.707

• -0.5

• 0.5

Why do sine values become negative beyond 180 degrees?

• Because the triangles are above the x-axis

• Because the triangles are below the x-axis

• Because the radius changes

• Because the angles are acute

What is the significance of the sine function's negative values?

• They are irrelevant to the function

• They are errors in calculation

• They represent angles greater than 180 degrees

• They indicate a change in radius