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Using the Unit Circle Reference Angles

HSF-TF.A.2
Answer Keys Here

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.

  • 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.