# Unit Circle Reference Angles Worksheets

The unit circle is a great tool to help you find measures of trigonometric functions in either units of radians or degrees. The unit circle is broken into four quadrants that each have their own distinct centered measures. When we find a measure located within a particular quadrant, we can use the terminal side of that angle and line it up with the x-axis to determine the measure of the reference angle. Reference angles are super helpful for determining the value of measures quickly. These worksheets and lessons in this section can be used to use specific angles to solve unique trig. problems.

### Aligned Standard: HSF-TF.A.2

- 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.

- Answer Keys - These are for all the unlocked materials above.

### 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.

- Quiz 1 - This quiz is a quick pick me up.
- Quiz 2 - You can work in the space that is provided, but you will need to spread out in the next one.
- Quiz 3 - These are common problem types.

### 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.

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 value of the trigonometric functions sine and cosine in right-angled triangles. It is a great tool that makes finding these values pretty simple and really simplifies the math that is involved with it. 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.

Reference angles serve as another helpful tool to simplify trigonometric calculations. Reference angles start from 0 degrees and go up to Π/2 within each quadrant. As a result, they are acute angles. It is an angle that is formed between the x-axis and the terminal side of a particular angle.

Depending on what quadrant these reference angles are located determines how we determine their measures. The only one that is simple is the first quadrant because angles there are their own reference angle. For any angle located in the second or third quadrant you determine the reference angle measure by subtracting it from 180 degrees or Π (for radians). For angles located in the fourth quadrant there reference angle can be determined by subtracting them from either 360 degrees or 2Π (for radians).