Trigonometric Functions and Ratios

The video tutorial explains trigonometric functions for general angles using the Pythagorean theorem. It covers the six trigonometric functions: sine, cosine, tangent, cosecant, secant, and cotangent, and their reciprocal relationships. Two examples are provided to demonstrate how to calculate these functions using points in standard position, focusing on the first and third quadrants. The tutorial emphasizes the importance of non-zero denominators to avoid undefined values.

What theorem is used to find the hypotenuse in trigonometric functions for general angles?

• Pythagorean theorem

• Remainder theorem

• Binomial theorem

• Fundamental theorem of calculus

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

• Secant

• Tangent

• Sine

• Cosine

What is the reciprocal of the sine function?

• Secant

• Tangent

• Cotangent

• Cosecant

In Example 1, what is the value of R for the point (-8, -6)?

• 6

• 12

• 8

• 10

For the point (-8, -6), what is the value of sine(theta)?

• -6/10

• -8/10

• 10/6

• 8/10

For the point (-8, -6), what is the value of cosine(theta)?

• -6/10

• -8/10

• 10/8

• 8/10

In Example 2, what is the value of R for the point (-3, -4)?

• 5

• 3

• 4

• 6

For the point (-3, -4), what is the value of tangent(theta)?

• -3/4

• 4/3

• 3/4

• -4/3

For the point (-3, -4), what is the value of secant(theta)?

• -4/5

• 5/-3

• -3/5

• 5/-4

For the point (-3, -4), what is the value of cotangent(theta)?

• -4/3

• -3/4

• 4/3

• 3/4