Understanding the Unit Circle and Reference Triangles

This video tutorial explores the unit circle and reference triangles using Desmos. It explains how trigonometric functions are defined on the unit circle, with a focus on angles and reference triangles of 30, 45, and 60 degrees in each quadrant. The tutorial also covers quadrantal angles, providing insights into their coordinates and trigonometric values. The Desmos tool is highlighted as a useful resource for visualizing these concepts.

What is the radius of the unit circle?

• 1 unit

• 3 units

• 0.5 units

• 2 units

In the unit circle, what is the value of cosine theta if the terminal side intersects at point (x, y)?

• x

• y

• 1/x

• 1/y

Which quadrant has both cosine and sine values positive for a 30-degree reference angle?

• First

• Third

• Fourth

• Second

In which quadrant is the cosine value negative and sine value positive for a 30-degree reference angle?

• First

• Second

• Third

• Fourth

What type of triangle is formed by a 45-degree reference angle in the unit circle?

• Obtuse

• Isosceles right

• Scalene

• Equilateral

In which quadrant are both x and y negative for a 45-degree reference angle?

• First

• Third

• Fourth

• Second

For a 60-degree reference angle, which quadrant has a positive x and negative y?

• First

• Second

• Third

• Fourth

What is the reference angle in the second quadrant for a 60-degree reference angle?

• 60 degrees

• 90 degrees

• 45 degrees

• 30 degrees

Which angle corresponds to the terminal side along the positive y-axis?

• 270 degrees

• 0 degrees

• 90 degrees

• 180 degrees

What are the x and y coordinates for the terminal side along the negative x-axis?

• (0, -1)

• (1, 0)

• (0, 1)

• (-1, 0)