Trigonometric Functions and Their Properties

The video tutorial introduces trigonometric functions for any angle, starting with common angles and special triangles. It explains the use of the unit circle and extends trigonometric functions to any angle using coordinates. The tutorial covers trigonometric ratios in right triangles and how to use the Pythagorean theorem to find the radius. It concludes with an introduction to reciprocal trigonometric functions.

What are the angles of a 30-60-90 triangle?

• 30, 30, 120 degrees

• 60, 60, 60 degrees

• 45, 45, 90 degrees

• 30, 60, 90 degrees

Why do we use the unit circle in trigonometry?

• To simplify calculations by using a radius of 2

• To ensure all angles are acute

• To have a consistent radius of 1 for calculations

• To avoid using any triangles

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

• Hypotenuse over opposite

• Adjacent over opposite

• Opposite over hypotenuse

• Adjacent over hypotenuse

How do you determine the radius when a point is not on the unit circle?

• By assuming it is 1

• By using only the x-coordinate

• By measuring directly

• By using the Pythagorean theorem

What is the cosine of an angle in terms of x, y, and r?

• r over x

• y over r

• x over y

• x over r

What is the tangent of an angle in terms of x and y?

• x over y

• r over y

• y over x

• r over x

What is the cosecant function in terms of r and y?

• r over x

• x over r

• r over y

• y over r

What is the secant function in terms of r and x?

• r over x

• y over r

• x over r

• r over y

What is the cotangent function in terms of x and y?

• r over y

• y over x

• x over y

• r over x

Which theorem is used to find the radius in a right triangle?

• Pythagorean theorem

• Sine rule

• Cosine rule

• Tangent rule