Understanding the Sine Function

The video tutorial explains the sine function as a ratio of the opposite side to the hypotenuse in a right triangle. It visualizes this concept using a triangle and reference angles, demonstrating how to evaluate the sine of different angles. Examples are provided to illustrate the evaluation process, and a correction is made to a typo in the examples. The video concludes by encouraging viewers to continue learning about mathematics.

What does the sine function represent in a right triangle?

• The ratio of the adjacent side to the hypotenuse

• The ratio of the hypotenuse to the opposite side

• The ratio of the opposite side to the hypotenuse

• The ratio of the opposite side to the adjacent side

In the context of the sine function, what is the hypotenuse?

• The side opposite the reference angle

• The longest side of the triangle

• The side adjacent to the reference angle

• The side opposite the 90-degree angle

Which side is opposite to the reference angle in a right triangle?

• The side adjacent to the reference angle

• The longest side of the triangle

• The side opposite the 90-degree angle

• The side opposite the reference angle

When evaluating the sine of angle C, which sides are involved?

• Adjacent and opposite

• Opposite and adjacent

• Adjacent and hypotenuse

• Opposite and hypotenuse

What is the role of the reference angle in evaluating the sine function?

• It identifies the adjacent side

• It identifies the opposite side

• It is not used in the sine function

• It determines the hypotenuse

For angle A, what is the sine function's output?

• The ratio of the opposite side to the adjacent side

• The ratio of the opposite side to the hypotenuse

• The ratio of the adjacent side to the hypotenuse

• The ratio of the hypotenuse to the opposite side

How do you label the sides of a triangle when using the sine function?

• Adjacent, hypotenuse, opposite

• Adjacent, opposite, hypotenuse

• Opposite, hypotenuse, adjacent

• Hypotenuse, opposite, adjacent

In the example on the left, what is the sine of angle A?

• 28/35

• 24/40

• 35/28

• 40/24

What is the sine of angle C in the example on the right?

• 35/28

• 28/35

• 40/24

• 24/40

What is the sine ratio for a triangle with an opposite side of 24 and a hypotenuse of 40?

• 28/35

• 40/24

• 35/28

• 24/40