Understanding the Unit Circle and Trigonometry

What is the radius of a unit circle?

• 10 units

• 0.5 units

• 2 units

• 1 unit

Tags

CCSS.HSG.C.B.5

CCSS.HSG.GPE.A.1

Which coordinates correctly represent a point on the unit circle along the x-axis?

• (-1, 0)

• (0, 1)

• (1, 0)

• (0, -1)

Tags

CCSS.HSF.TF.A.3

What direction does a positive angle move in on the unit circle?

• Counterclockwise

• Clockwise

• Upwards

• Downwards

Tags

CCSS.HSF.TF.A.2

What are the coordinates of the intersection point of the terminal side of a positive angle theta with the unit circle?

• (1, 0)

• (0, 1)

• (b, a)

• (a, b)

Tags

CCSS.HSF.TF.A.3

CCSS.HSF.TF.C.8

What does the cosine of an angle theta represent in the context of the unit circle?

• The y-coordinate of the intersection point

• The x-coordinate of the intersection point

• The radius of the circle

• The length of the tangent line

Tags

CCSS.HSF.TF.A.2

CCSS.HSF.TF.A.3

CCSS.HSF.TF.C.8

How is the sine of an angle theta defined using the unit circle?

• The x-coordinate of the intersection point

• The length of the tangent line

• The radius of the circle

• The y-coordinate of the intersection point

Tags

CCSS.HSF.TF.A.2

CCSS.HSF.TF.A.3

CCSS.HSF.TF.C.8

What is the length of the hypotenuse in the right triangle formed within the unit circle?

• The same as the adjacent side

• 1 unit

• 2 units

• The same as the opposite side

Tags

CCSS.HSF.TF.C.8

CCSS.HSG.SRT.C.6

CCSS.HSG.SRT.C.8

What is the tangent of an angle theta defined as in the unit circle context?

• Sine of theta over cosine of theta

• The radius over the diameter

• Cosine of theta over sine of theta

• The x-coordinate over the y-coordinate

Tags

CCSS.HSF.TF.A.2

CCSS.HSF.TF.A.3

CCSS.HSF.TF.C.8

CCSS.HSG.SRT.C.6

What problem does the SOH CAH TOA definition encounter with angles of 90 degrees or more?

• It provides multiple values

• It cannot define trig functions for these angles

• It remains consistent

• It defines them as negative values

Tags

CCSS.HSF.TF.A.2

Why is the unit circle used to extend the definitions of trigonometric functions?

• To reduce the number of functions

• To simplify calculations

• To provide definitions for all angle measures

• To focus only on acute angles

Tags

CCSS.HSF.TF.A.2

CCSS.HSF.TF.A.3

CCSS.HSF.TF.A.4