Using the Unit Circle

PC_Week 6 - The Unit Circle

This week we will use the graphs of the Sine and Cosine functions to create the Unit Circle. The Unit Circle is a tool we will use often to evaluate the values of the trigonometric functions.

Monday's Do Now

Answer the next five questions in Quizizz. Let me know in the zoom chat, when you are done.

Multiple Choice

Use the figure to complete the following. 

1. 2π = 

• $$0\degree$$   
  

• $$90\degree$$  

• $$180\degree$$  

• $$360\degree$$  

Multiple Choice

Use the figure to complete the following. 

2. 180⁰ = ____________ 

• $$\frac{\pi}{2}$$   
  

• $$\pi$$  

• $$2\pi$$  

Multiple Choice

Use the figure to complete the following. 

3. Cos(x) at 0⁰ = ________

• 0

• 1

• -1

Multiple Choice

Use the figure to complete the following. 

4. Sin(x) at π/2 = _________ 

• 0

• 1

• -1

Multiple Select

Use the figure to complete the following. 

5. Identify 2 locations where Sin(x) = Cos(x) ________ & _________

• $$45\degree\ and\ \ 225\degree$$

• $$0\degree\ and\ \ 2\pi$$  

• $$\frac{\pi}{4}\ and\ \frac{5\pi}{4}$$  

Sine and Cosine Table of Values

Use the graphs of the Sine and Cosine Functions to complete the Table of Values on page 1 of the Unit Circle_Classwork 6 assignment.

The link is in google Classroom.

Degrees & Radians

Video: Introduction to the Unit Circle

We will learn to create and convert (degrees to radians) the angles on the Unit Circle.

180⁰ = π

Multiple Choice

Which is the equivalent of $$\frac{\pi}{2}$$ ? 

• 0°

• 30°

• 90°

• 270°

Multiple Choice

Which is the equivalent of $$\frac{3\pi}{2}$$ ? 

• 0°

• 30°

• 90°

• 270°

Multiple Choice

Which is the equivalent of $$\frac{3\pi}{4}$$ ? 

• 135°

• 225°

Multiple Choice

Which is the equivalent of $$\frac{5\pi}{4}$$ ? 

• 135°

• 225°

Multiple Choice

Which is the equivalent of $$\frac{\pi}{6}$$ ? 

• 30°

• 150°

Multiple Choice

Which is the equivalent of $$\frac{5\pi}{6}$$ ? 

• 30°

• 150°

Multiple Choice

Which is the equivalent of $$\frac{\pi}{3}$$ ? 

• 30°

• 60°

Multiple Choice

Which is the equivalent of $$\frac{4\pi}{3}$$ ? 

• 60°

• 240°

Create the Unit Circle, Part 1

Now that we know how to convert degrees to radians, let begin to build our Unit Circle.

On page 2 of the Unit Circle_Classwork 6 assignment in google classroom, enter in all of the angle measures on the Unit Circle. Use the text box tool to make your entries.

Tuesday

Tuesday's Do Now

Answer the next five questions in Quizizz. Let me know in the zoom chat, when you are done.

Multiple Choice

1. In which quadrant does each angle or radian lie?

A. 80⁰

• 1

• 2

• 3

• 4

Multiple Choice

2. In which quadrant does each angle or radian lie?

B. 5π/3

• 1

• 2

• 3

• 4

Multiple Choice

3. In which quadrant does each angle or radian lie?

C. - 210⁰

• 1

• 2

• 3

• 4

Create the Unit Circle, Part 2

The second main component of the Unit Circle is the coordinate pair, (x,y), of each angle. The coordinates represent the Cosine and the Sine values for each angle.

Since the radius of the Unit Circle is 1, we can easily write the coordinates out for the five quadrantal angles - angles that end on the x- or y-axis. On page 3 of the Unit Circle_Classwork 6 assignment in google classroom, enter the quadrantal coordinates.

Multiple Choice

What is the sin(90^o)?

• 0

• 1

• -1

Multiple Choice

What is the cos(180^o)?

• 0

• 1

• -1

Multiple Choice

What is the sin( $$\frac{3\pi}{2}$$ )? 

• 0

• 1

• -1

Multiple Choice

What is the cos(2𝜋)?

• 0

• 1

• -1

Create the Unit Circle, Part 2

We will use what we learned in Geometry (SOH-CAH-TOA) to help us find the exact sine and cosine values for the 30°, 45° and 60° angles - and their cooresponding reference angles around the Unit Circle.

Complete the table on page 4 of the Unit Circle-Classwork 6 assignment.

Create the Unit Circle, Bringing It All Together

You will use all that you learned this week to build a complete Unit Circle on pages 5 and 6 of the Unit Circle Classwork 6 Assignment.

Thursday's Do Now

Find each exact value.

Put answers in zoom chat.

1. Sin (π)

2. Cos (30⁰)

3. Tan (135⁰)

****Hint: tan(x) = sin(x)/cos(x)

4. Tan (60⁰)

5. Sin (11π/6)

6. Cos (5π/4)

Create the Unit Circle, Bringing It All Together

You will need to know how to use the Unit Circle to EVALUATE the sine, cosine and tangent (sine/cosine) function values.

Multiple Choice

$$\sin\left(240\degree\right)$$  

• $$-\frac{1}{2}$$  

• $$-1$$  

• $$-\frac{\sqrt{3}}{2}$$  

• $$\frac{1}{2}$$  

Multiple Choice

Which angle measure corresponds to the ordered pair of

$$\left(\frac{\sqrt{2}}{2},-\frac{\sqrt{2}}{2}\right)$$  

• $$315\degree$$  

• $$\frac{3\pi}{4}$$  

• $$225\degree$$  

• $$\frac{\pi}{4}$$  

Multiple Choice

Which angle measure corresponds to the ordered pair of

$$\left(1,0\right)$$  

• $$90\degree$$  

• $$\frac{3\pi}{2}$$  

• $$180\degree$$  

• $$2\pi$$  

Multiple Choice

$$\sin\left(\frac{\pi}{2}\right)$$  

• $$-1$$  

• $$\frac{\sqrt{2}}{2}$$  

• $$1$$  

• $$-\frac{\sqrt{3}}{2}$$  

Multiple Choice

$$\cos\left(315\degree\right)$$  

• $$\frac{\sqrt{3}}{2}$$  

• $$-\frac{1}{2}$$  

• $$0$$  

• $$\frac{\sqrt{2}}{2}$$  

Multiple Choice

$$\cos\left(\frac{\pi}{6}\right)$$  

• $$\frac{\sqrt{3}}{2}$$  

• $$\frac{1}{2}$$  

• $$\frac{\sqrt{2}}{2}$$  

• $$0$$  

Multiple Choice

What is the exact value of $$\cos\ 150\degree$$  ?

• $$\frac{\sqrt{3}}{2}$$  

• $$\frac{1}{2}$$  

• $$-\frac{\sqrt{3}}{2}$$  

• $$-\frac{1}{2}$$  

Multiple Choice

135° is found in which quadrant?

• Quadrant 1

• Quadrant 2

• Quadrant 3

• Quadrant 4

Multiple Choice

What is the radius of a unit circle?

• 1

• 2

• 1/2

• 0

Multiple Choice

• √3/3
• √3
• 1
• undefined

Multiple Choice

How many degrees is ^π/₄ radians?

• 30°

• 45°

• 60°

• 90°

Multiple Choice

How many degrees is ^π/₆ radians?

• 90°
• 60°
• 45°
• 30°

Multiple Choice

What is cos 90°?

• ½
• undefined
• 1
• 0

Multiple Choice

What is cos 60°?

• ½

• ^√3/₂

• ^√2/₂

• 1