Using the Unit Circle

Using the Unit Circle (M3 Basic)

What can this thing do?

In this lesson, we will use the unit circle to:

• Find exact trig values of any angle

• Use special right triangles to find these exact values

What special right triangles?!

• The 45-45-90

• The 30-60-90

The 30-60-60

Draw it!

The 45-45-90

Yes, draw it too!

Fill in the Blank

Find the measure of side x:

Multiple Choice

Find the value of side h:

• $$1$$

• $$2$$

• $$\sqrt{2}$$

• $$\sqrt{3}$$

Multiple Choice

Find the measure of side y:

• 1

• 2

• $$\sqrt{3}$$

• $$\sqrt{2}$$

Fill in the Blank

Find the measure of side h:

Notebooks ready!

You will turn in the Step-by-Step Solving of

 $\sin\left(\frac{3\pi}{4}\right)$  

Multiple Choice

How many degrees is ^π/₃ radians?

• 30°
• 45°
• 60°
• 90°

Multiple Choice

How many degrees is ^π/₆ radians?

• 90°
• 60°
• 45°
• 30°

Fill in the Blank

What would be the reference angle for 300 degrees?

Type your answer in degrees (but not the word degrees).

More Examples to follow

• Draw the diagrams

• These do not have to be on the submitted notes

Fill in the Blank

What is the reference angle, in degrees, for 315?

For the last slides/questions...

• Pull up, print, or draw a complete Unit Circle with angles (degrees and radians) and coordinates

• Use it to help you answer the questions.

Multiple Choice

What is the cosine of $$390\degree$$  

• 30

• $$\frac{\sqrt{3}}{2}$$  

• $$\frac{1}{2}$$  

• $$\frac{\pi}{6}$$  

Multiple Choice

What is the cosine of $$-\frac{\pi}{3}$$  radians

• $$\frac{\sqrt{3}}{2}$$  

• $$\frac{5\pi}{3}$$  

• $$\frac{1}{2}$$  

• $$-\frac{\sqrt{2}}{2}$$  

Fill in the Blank

Type an angle measure between 0 and 360 which has a cosine value of

$$-\frac{1}{2}$$  

Multiple Choice

tan 225º

• 1

• -1

• 0

• undefined

Multiple Choice

10π/9  is equal to how many degrees?

• 100°
• 140°
• 190°
• 200°

Multiple Choice

How many radians in a full circle?

• π/2
• π
• 3π/2
• 2π

Multiple Choice

What is cos 90°?

• ½
• undefined
• 1
• 0

Multiple Choice

What is the cosine of $$390\degree$$  

• 30

• $$\frac{\sqrt{3}}{2}$$  

• $$\frac{1}{2}$$  

• $$\frac{\pi}{6}$$  

Fill in the Blank

Find the exact value:

$$\tan\left(315\right)$$  
(Angle is given in degrees.)

Fill in the Blank

Find the exact value:

$$\cos\left(\pi\right)$$  

(Angle given in radians.)