Trigonometric Functions and Unit Circle

This video tutorial from Higher Math Solutions explains how to evaluate trigonometric functions using the unit circle. It covers the basics of the unit circle, including key points and angles, and explains how to use 30-60-90 and 45-45-90 triangles for quick evaluations. The video also includes practice problems and advanced examples, demonstrating how to rationalize answers and apply trigonometric concepts effectively.

What is the primary advantage of using right triangles over recreating the entire unit circle?

• It is more accurate.

• It is faster and more efficient.

• It requires less memorization.

• It provides a better understanding of angles.

What are the coordinates of the point at 0 degrees on the unit circle?

• (1, 0)

• (0, 1)

• (0, -1)

• (-1, 0)

In a 30-60-90 triangle, what is the length of the long leg if the hypotenuse is 1?

• √3/2

• 1/2

• √2/2

• 1

Which angle corresponds to π/4 radians in the unit circle?

• 30 degrees

• 90 degrees

• 45 degrees

• 60 degrees

What is the sine of 3π/2 on the unit circle?

• √3/2

• -1

• 1

• 0

How do you calculate the tangent of an angle using the unit circle?

• Y/X

• X+Y

• X*Y

• X/Y

What is the cosine of 5π/6?

• -1/2

• -√3/2

• 1/2

• √3/2

In which quadrant is 5π/6 located?

• First

• Second

• Third

• Fourth

What is the cosecant of π/3?

• 2

• √3/2

• 1/√3

• 2/√3

Why is it necessary to rationalize the denominator in trigonometric calculations?

• To avoid division by zero

• To ensure the result is a real number

• To make calculations easier

• To simplify the expression