Trigonometric Functions and Their Properties

This video tutorial introduces trigonometric functions in terms of angles of rotation. It explains how to define sine, cosine, and tangent using a reference triangle and discusses the impact of different quadrants on the sign of these functions. The tutorial includes example problems to illustrate the concepts and demonstrates the use of the unit circle to simplify calculations. The video concludes with a final example and a summary of key points.

What is the hypotenuse of a right triangle formed by an angle in standard position intersecting a circle at point (x, y)?

• x + y

• r

• y

• x

What is the reciprocal of the sine function known as?

• Secant

• Tangent

• Cosecant

• Cotangent

In which quadrant are both x and y coordinates positive, making all trigonometric functions positive?

• Fourth Quadrant

• Third Quadrant

• Second Quadrant

• First Quadrant

In the third quadrant, what is the sign of the tangent function?

• Zero

• Undefined

• Negative

• Positive

What is the value of r when using the unit circle to find trigonometric functions?

• 0

• 1

• x

• y

What is the cosine of 90 degrees on the unit circle?

• -1

• 0

• Undefined

• 1

Which angle is considered a quadrantal angle?

• 30 degrees

• 45 degrees

• 60 degrees

• 90 degrees

What is the tangent of 90 degrees on the unit circle?

• 0

• 1

• Undefined

• Square root of 3

What is the sine of a 60-degree angle on the unit circle?

• 1/2

• Square root of 3/2

• 0

• 1

What is the value of cotangent for a 60-degree angle on the unit circle?

• 1/Square root of 3

• 0

• 1

• Square root of 3