Reference Angle in Unit Circle

Creating the Unit Circle

By Stephanie Balbaneda

​Last class we covered the creating of the Unit Circle

​Today you will be able to create the unit circle on your OWN

​But first,

lets Review ​......

Reference Angle

• A reference angle is an angle in standard position on the coordinate plane

• Standard Position: positive acute angle where initial side is on the positive x-axis and terminal side is in quadrant one.

How to find Reference Angles

• Quadrant 1: Angle Measure = Reference Angle

• Quadrant 2: 180 - Angle Measure

• Quadrant 3: Angle Measure - 180

• Quadrant 4: 360 - Angle Measure

Reference Angle Example

Multiple Choice

What is the reference angle?

• 43

• -43

• 47

• -47

Multiple Choice

What is the reference angle for 63°?

• 117°

• 207°

• 63°

• 153°

Multiple Choice

What is the reference angle for -30°?

• 150°

• 30°

• 80°

• 60°

Multiple Choice

What is the reference angle for 125°?

• 235°

• 125°

• 75°

• 55°

Coterminal Angle

What is the unit circle?

• It is a circle centered at the origin (0,0) with a radius of 1

• It has the formula x² + y² = 1

• It is a shortcut to finding the sine and cosine of the angles of special right triangles (30-60-90) or (45-45-90)

Multiple Choice

Which is the length of the radius of a unit circle?

• $$\frac{1}{2}$$

• $$1$$

• $$\frac{\sqrt{2}}{2}$$

• $$\frac{\sqrt{3}}{2}$$

Special Right Triangles

45-45-90 and the 30-60-90

45-45-90

30 - 60 - 90

Why do I need to learn this?

The Unit Circle

The unit circle is used to understand sine and cosine angles found in right triangles. The center is at the origin (0,0) and has a radius of one unit.

The radius goes through a coordinate on the circumference of the circle and has coordinates of (cosθ, sinθ)​

​Looking at the backbone of unit circle

Used to organize the stars and give them coordinates

Trig functions originated in trig

​

​Astronomy

Used to determine geometric patterns in buildings

Curving surfaces (like glass or steel)

Finding Heights

Creating 3-D figures​

Architecture

Real World Applications

Some text here about the topic of discussion

​Real World Applications Continued...

The unit circle has helped with digital imaging, such as computer graphics, voice to text, or photography.

Also, it helped predict movements of water, light, and sound.​

Multiple Choice

What trig functions make up the coordinates in the unit circle?

• cosine and sine

• only sine

• only cosine

• sine, cosine, and tangent

Values for the Cosine and Sine

A Couple of Things to Notice

Multiple Choice

Which type of triangle can be used to create an angle of π/3?

• equilateral triangle

• acute triangle

• 45°-45°-90°

• 30°-60°-90°

Multiple Choice

At what point are sine and cosine the same value?

• 0

• 90

• 45

• 60