Coterminal Angles, Unit Circle Trig with Radians and Degrees

Degrees and Radians

Multiple Choice

Convert 150⁰ to radians

• 5π/6
• 3π/4
• 7π/6
• 2π/3

Multiple Choice

Convert π radians to degrees.

• 90⁰
• 180⁰
• 360⁰
• 60⁰

Multiple Choice

Find a coterminal angle to 5°.

• 365°

• 255°

• -220°

• -365°

1. Reference Angle (α)

• Any angle around a circle can be turned into a right triangle using a reference angle (α).

• Using this we can calculate any angle around the center of a circle.

• Depending on the Quadrant (I, II, III, IV) the initial side of the refence angle changes.

​How to find the angle using a reference angle by quadrant:

Multiple Choice

What is the reference angle for 125°?

• 235°

• 125°

• 75°

• 55°

Multiple Choice

What is the reference angle for 275°?

• 85°

• 95°

• -85°

• -95°

Multiple Choice

What is the reference angle for 63°?

• 117°

• 207°

• 63°

• 153°

Multiple Choice

What is the reference angle?

• 163

• 73

• 27

• 107

Multiple Choice

What is the reference angle?

• 43

• -43

• 47

• -47

Poll

What do you think of the Quizizz lesson, so far?

• Never do this again

• I don't care

• Let's do it again!

• This should be every lesson

Evaluating Sine & Cosine with the Unit Circle

Goal: Students will be able to evaluate sine and cosine using the Unit Circle

Using the Unit Circle

• to evaluate sine and cosine, we use the coordinates that lie on the Unit Circle's circumference

• cosine of an angle is equal to the length of the reference triangle's adjacent side and is represented by the x-coordinate

• sine of an angle is equal to the length of the reference triangle's opposite side and is represented by the y-coordinate

Evaluating Cosine

• cos(θ) = x-coordinate of the point associated with that angle

• cos(270°) = 0

• cos(π/6) = √3/2

• cos(2π/3) = -1/2

Multiple Choice

Evaluate cos(135°)

• $$-\frac{\sqrt{2}}{2}$$  

• $$\frac{\sqrt{2}}{2}$$  

• $$-\frac{\sqrt{3}}{2}$$  

• $$-\frac{1}{2}$$  

• $$\frac{\sqrt{3}}{2}$$  

Open Ended

List 3 things you know about circles. It may include its definition, parts and equation.

The Unit Circle

Dropdown

What makes a unit circle, a UNIT CIRCLE?

A unit circle is ​

Select answer

in which the ​

Select answer

is found at ​

Select answer

with a ​​ radius of ​ ​

Select answer

.

Redefining the Six Trigonometric Functions
Using x, y and r on the Unit Circle

Interactive Notes

Evaluating the Six Trigonometric Functions Of
Quadrantal Angles

Example 1: Evaluate sin, cos, tan, csc, sec and
cot 90⁰.

Evaluating the Six Trigonometric Functions Of
Quadrantal Angles

Example 1: Evaluate sin, cos, tan, csc, sec and
cot 90⁰.

Match

Match the following

• sin 180^o

• sec 180^o

• cos 360^o

• tan -90^o

0

-1

1

undefined

• 0

• -1

• 1

• undefined

Poll

Which objectives do you fully understand?

• Define what is a Unit Circle.

• Define the 6 Trig Ratios using x, y and r.

• Solve the six Trigonometric Functions of Quadrantal Angles

Poll

Which objectives do you need clarification?

• Define what is a Unit Circle.

• Define the 6 Trig Ratios using x, y and r.

• Solve the six Trigonometric Functions of Quadrantal Angles

• None

Multiple Choice

Evaluate cos(11π/6)

• $$-\frac{\sqrt{2}}{2}$$  

• $$\frac{\sqrt{2}}{2}$$  

• $$-\frac{\sqrt{3}}{2}$$  

• $$-\frac{1}{2}$$  

• $$\frac{\sqrt{3}}{2}$$  

Evaluating Sine

• sin(θ) = y-coordinate of the point associated with that angle

• sin(4π/3) = -√3/2

• sin(0) = 0

• sin(135°) = √2/2

Multiple Choice

Evaluate sin(60°)

• 0

• $$\frac{1}{2}$$  
  

• $$\frac{\sqrt{2}}{2}$$  
  

• $$\frac{\sqrt{3}}{2}$$  

• 1

Multiple Choice

sin(7π/6)

• - ½

• √3 /2

• ½

• -√3 /2

• -√2 /2

Multiple Choice

sin 180°

• 1

• -1

• 0

• $$-\frac{\sqrt{3}}{2}$$

• $$\frac{1}{2}$$

Multiple Choice

What is the exact coordinates of 3π/4 on the unit circle?

• (−√2∕2, √2∕2)

• (−√2∕2, −√2∕2)

• (−√3∕2, −√2∕2)

• (√2∕2, −√2∕2)

Multiple Choice

cos(π)=

• 0

• 1

• -1

• 1/2

Multiple Choice

cos (π/4)

• √3/2

• √2/2

• 1/2

• 1

Multiple Choice

sin π/4

• √2∕2

• 1/2

• √3/2

• 0