Trigonometric Functions and Their Properties

The video tutorial explains angles in standard position, forming right triangles, and using the Pythagorean theorem to find the hypotenuse. It defines six trigonometric functions of an angle, theta, and demonstrates these concepts through an example problem, calculating the exact values of trigonometric functions for a given point on the terminal side.

What is the initial side of an angle in standard position?

• The side that lies on the y-axis

• The side that lies on the x-axis

• The side that lies on the z-axis

• The side that lies on the terminal side

In which quadrant is the terminal side placed in the example?

• Fourth quadrant

• Second quadrant

• First quadrant

• Third quadrant

What shape is formed when a point on the terminal side is extended to the x-axis?

• A circle

• A right triangle

• A rectangle

• A square

What is the relationship between x, y, and r in the Pythagorean theorem?

• x + y = r^2

• x^2 - y^2 = r^2

• x^2 + y^2 = r^2

• x^2 + y^2 = r

Which trigonometric function is defined as opposite over hypotenuse?

• Sine

• Tangent

• Cotangent

• Cosine

What is the point given on the terminal side in the example problem?

• (3, 4)

• (4, 3)

• (-3, 4)

• (3, -4)

What is the value of r calculated using the Pythagorean theorem in the example?

• 6

• 5

• 4

• 3

What is the sine of theta for the example problem?

• 4/3

• -4/5

• 3/5

• 5/3

What is the cosine of theta for the example problem?

• -4/5

• 3/5

• 5/3

• 4/3

What is the tangent of theta for the example problem?

• 4/5

• 5/4

• 3/4

• -4/3