Trigonometric Functions and Angles

The video tutorial explains how to determine the exact trigonometric function values for 1,470 degrees using reference triangles. It covers the properties of 30-60-90 and 45-45-90 triangles, sketches the angle in standard position, and calculates cosine, sine, tangent, and cotangent values. The tutorial also demonstrates how to verify these values using the unit circle.

What are the two main methods to determine trig function values for angles?

• Using a compass or a ruler

• Using a graph or a table

• Using a calculator or a protractor

• Using a unit circle or reference triangles

In a 30-60-90 triangle, what is the ratio of the short leg to the hypotenuse?

• 1:√2

• 1:1

• 1:2

• 1:√3

What is the length of the hypotenuse in a 45-45-90 triangle if each leg is 1?

• √2

• 2

• √3

• 1

How many complete revolutions are made to sketch 1,470 degrees in standard position?

• 3

• 4

• 5

• 6

What is the reference angle for 1,470 degrees?

• 90 degrees

• 45 degrees

• 60 degrees

• 30 degrees

What is the cosine of the reference angle using the reference triangle?

• √3/2

• √2/2

• 1/2

• 1

What is the sine of the reference angle using the reference triangle?

• 1

• √3/2

• 1/2

• √2/2

What is the tangent of the reference angle before rationalization?

• 1/2

• √3/1

• 1/√3

• 2/√3

What is the cotangent of the reference angle after rationalization?

• 2/√3

• 1/2

• 1/√3

• √3

How can the trigonometric values be verified using the unit circle?

• By drawing a graph

• By checking the intersection of the terminal side with the unit circle

• By using a calculator

• By measuring angles with a protractor