Name: 4-1 Unit Circle and Exact Values Learning Goals: 1) How can we use the unit circle to find the value of sine, cosine, and tangent? 2) Given a point on a circle and the radius of the circle, how can we determine sine and cosine? Warm up: Unit circle Fill in the exact values for quadrant 1 reference angles. Re-activate: TANGENT Example 1)Determine the exact value for: a) Together: tan π 6 b) You try! tan π 3
Practice with Reference Angles! Example #2a: i) Sketch the angle ii) Shade the reference angle iii) State the measure of the reference angle 1) 120 o 2) 5π 3 Example #2b: i) Sketch the angle ii) Shade the reference angle iii) State the measure of the reference angle 1) 210 o 2) 3π 4 Basic Values from Quadrant I of the unit circle 3. Find the exact value of: a) Cos45 b) tan60 c) sin-135 d) cos270 e) sin( π 4 )+ sin( π 3 )
Loop 1: Evaluating Expressions Using Exact Values In your pairs work on the following problems together. Collaborate with each other and check answers. Don t forget to show all work. 1. cos 4π 3 2. cos 3π 4 3. sin225 o Work on this set of problems individually. DO NOT WORK WITH YOUR PARTNER until both of you are done with this section. Once both partners are completed, check answers with one another then move on to the next loops. Do not progress without your partner. 4. sin 5π 6 5. tan225 6. cos 11π 6
Loop 2: Evaluating 2-step Expressions Using Exact Values In your pairs work on the following problems together. Collaborate with each other and check answers. Don t forget to show all work. 1. 1-sin 2 ( π 6 ) 2. cos 4π 3 + tan225 3. 2sin π 6 cos π 6 4. cos( π 3 ) - cos( π 6 ) Work on this set of problems individually. DO NOT WORK WITH YOUR PARTNER until both of you are done with this section. Once both partners are completed, check answers with one another then move on to the next loops. Do not progress without your partner. 5. sin( π 4 )+ sin( π ) 6. sin 5π 3 + tan 5π 7. cos (sinπ) 4 6
1) Determine the exact values for: 4-1 Homework Name: (a) sin 5π 4 (b)tan 5π 6 (c) sin135 o (d) cos180 (e) tan π 3 (f) cos90 (g) sin( 5π 3 ) 2) Evaluate the following by simplifying as far as possible: 3) Show that: cos( π 3 ) - cos( π 6 ) Sneak Peak! 1. Solve for x, such that 0 o < x < 360 o. Show all work! Sin(x) + 2 = 3 Don t forget to check the key!
Watch the assigned video fill in notes/answer questions as you go. Mastery of the content of this video is essential for you to understand in class. Content in this video is only covered in this assignment. I WILL NOT TEACH THIS CONTENT in a separate lesson during class. You can re-watch parts at any time and if you have questions. Apply it! Using this relationship, how might we be able to figure out the number of radians that equate to 60 o? LEAVE IN TERMS OF PI! **Note: Always leave radians in terms of π, and as a reduced fraction, unless otherwise specified. *SET UP PROPORTION:* π = radians measure 180 degree measure You try: Convert 45 degrees to radians! LEAVE IN TERMS OF PI! Try two more! Convert: 135 degrees = radians degrees = 5π 6 radians