Trigonometric Functions in Right Triangles

This video tutorial by Paul introduces the trigonometric functions sine, cosine, and tangent, explaining their relationships with the sides of a right triangle. It covers the definitions and calculations of these functions, illustrating how sine is the ratio of the opposite side to the hypotenuse, cosine is the ratio of the adjacent side to the hypotenuse, and tangent is the ratio of the opposite side to the adjacent side. The video also explains how tangent can be expressed as sine divided by cosine, and provides an example calculation using a right triangle with specific side lengths.

What is the side opposite the 90° angle in a right triangle called?

• Base

• Hypotenuse

• Adjacent

• Opposite

Which trigonometric function is defined as the ratio of the opposite side to the hypotenuse?

• Cosine

• Sine

• Tangent

• Secant

How is the cosine of an angle in a right triangle calculated?

• Opposite divided by Adjacent

• Adjacent divided by Hypotenuse

• Opposite divided by Hypotenuse

• Hypotenuse divided by Opposite

What is the tangent of an angle in a right triangle?

• Hypotenuse divided by Adjacent

• Adjacent divided by Hypotenuse

• Opposite divided by Hypotenuse

• Opposite divided by Adjacent

How can the tangent of an angle also be expressed?

• Cosine minus Sine

• Sine multiplied by Cosine

• Cosine divided by Sine

• Sine divided by Cosine

In the example problem, what is the length of the hypotenuse?

• 3

• 4

• 5

• 6

What is the sine of theta in the example problem?

• 3/5

• 5/3

• 4/5

• 5/4

What is the cosine of theta in the example problem?

• 5/4

• 5/3

• 3/5

• 4/5

What is the tangent of theta in the example problem?

• 5/3

• 4/3

• 3/4

• 5/4

Which method was used to verify the tangent calculation in the example?

• Cosine minus Sine

• Cosine over Sine

• Sine times Cosine

• Sine over Cosine