Trigonometric Functions and Their Properties

The video tutorial explains how to evaluate trigonometric expressions using reference triangles, focusing on angles in the first quadrant. It reviews right triangle trigonometry, including sine, cosine, and tangent ratios. The tutorial demonstrates simplifying expressions like sine of pi/3, inverse sine of cosine pi/4, and inverse sine of cosine pi/6 using 30-60-90 and 45-45-90 triangles. It also covers evaluating sine of pi/2 using the unit circle and sine graph.

What is the significance of using reference triangles in trigonometry?

• They simplify calculations for angles in the first quadrant.

• They are only used for angles greater than 90 degrees.

• They help in visualizing angles in any quadrant.

• They are used to convert degrees to radians.

Which of the following is the correct definition of the sine function in right triangle trigonometry?

• Ratio of the hypotenuse to the opposite side.

• Ratio of the opposite side to the hypotenuse.

• Ratio of the opposite side to the adjacent side.

• Ratio of the adjacent side to the hypotenuse.

How do you determine the sine of pi/3 using a 30-60-90 triangle?

• By using the ratio of the adjacent side to the hypotenuse.

• By using the ratio of the opposite side to the adjacent side.

• By using the ratio of the opposite side to the hypotenuse.

• By using the ratio of the hypotenuse to the adjacent side.

What is the inverse cosine of square root three divided by two?

• 45 degrees or pi/4 radians

• 30 degrees or pi/6 radians

• 90 degrees or pi/2 radians

• 60 degrees or pi/3 radians

Which angle corresponds to the inverse sine of one divided by square root two?

• 90 degrees or pi/2 radians

• 60 degrees or pi/3 radians

• 45 degrees or pi/4 radians

• 30 degrees or pi/6 radians

What is the cosine of pi/4 radians using a 45-45-90 triangle?

• 1 divided by 2

• Square root 2 divided by 2

• Square root 3 divided by 2

• 1 divided by square root 2

How is the sine of pi/2 radians evaluated using the unit circle?

• By finding the x-coordinate of the point on the unit circle.

• By finding the y-coordinate of the point on the unit circle.

• By finding the distance from the origin to the point on the unit circle.

• By finding the angle between the x-axis and the point on the unit circle.

What is the inverse cosine of one?

• 360 degrees or 2pi radians

• 90 degrees or pi/2 radians

• 180 degrees or pi radians

• 0 degrees or 0 radians

Which of the following angles is a quadrantal angle?

• 45 degrees

• 30 degrees

• 90 degrees

• 60 degrees

What is the sine function value at pi/2 radians?

• 0

• 1

• -1

• Square root 2 divided by 2