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

Tags

CCSS.HSF.TF.A.2

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

Tags

CCSS.HSF.TF.A.2

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

• First

• Third

• Fourth

• Second

Tags

CCSS.HSF.TF.A.2

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

• First

• Second

• Third

• Fourth

Tags

CCSS.HSF.TF.A.2

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

• Obtuse

• Isosceles right

• Scalene

• Equilateral

Tags

CCSS.HSF.TF.A.2

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

• First

• Third

• Fourth

• Second

Tags

CCSS.HSF.TF.A.2

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

• First

• Second

• Third

• Fourth

Tags

CCSS.HSF.TF.A.2

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

Tags

CCSS.5.G.A.1

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

• (0, -1)

• (1, 0)

• (0, 1)

• (-1, 0)

Tags

CCSS.5.G.A.1