## Using the Unit Circle Reference Angles

#### Aligned To Common Core Standard:

**High School** - HSF-TF.A.2

What are Unit Circle Reference Angles? The concept of unit circles and reference angles are crucial in solving trigonometric problems in mathematics. There are a variety of different uses cases in real life of unit circles and reference angles such as architecture, digital imaging, geography, engineering, and astronomy. So, what is a unit circle? A unit circle is drawn with the origin as its center and a radius of one unit. The primary purpose of this circle is to help people in understanding the sines and cosines in right-angled triangles. The positive x-axis serves as the reference line to measure the angles. It helps in finding the solutions to trigonometric problems in a short time, without the messy calculations. The angles in the unit circle can be written in both radians and degrees. Coming to the next important concept in trigonometry – reference angles. Reference angles serve as another helpful tool to simplify trigonometric calculations. Reference angles start from 0 degrees and go up to Π/2. It is an angle that is formed between the x-axis and the terminal side of a particular angle. These worksheets and lessons in this section can be used to use specific angles to solve unquie trig. problems.

### Printable Worksheets And Lessons

- Capital T Typo Step-by-step
Lesson - This is an intended typo. The problem is looking for
a lower case letter, while the reference letter is upper case. It
is a good exercise.

- Guided Lesson
- Again, a purposeful typo. It is good to get students in the habit
of identifying this. I saw this happen on several national exams.

- Guided Lesson Explanation
- Inverse sin questions are very difficult for many people. See
if this helps.

- Practice Worksheet
- A few of these are trick questions to see if students are paying
attention.

- Matching Worksheet
- This isn't too difficult to work through. It should be second
nature by now.

#### Homework Sheets

Focus on the meaning and purpose of the unit circle.

- Homework 1 - In each part we begin by finding the reference angle corresponding to the a given real number.
- Homework 2 - Since 390° is greater than 360°, we find a coterminal angle t, greater than zero and less than 360°, to 390°.
- Homework 3 - sec (3 π / 4) has terminal side in quadrant 2 the secant is negative.

#### Practice Worksheets

Determine the exact value of what you are presented with.

- Practice 1 - Find the exact values of cos (-180°).
- Practice 2 - Find the exact values of sin t and cos t for the given real number. T = 3π/2
- Practice 3 - These can be used to solve complex trig. problems.

#### Math Skill Quizzes

Are they all real numbers? This a question I hear often.