Pass out the Special Right Triangles Review worksheet. This is intended to remind students of the relationship between the sides of special right triangles 30° - 60° -90° and 45° - 45° - 90°. They are asked to use the Pythagorean Theorem to find a missing side and then to look at the result to remember the relationship. (This is a skill from Geometry, therefore, this activity is intended as simply a review of the topic.)
Allow students time to talk with other students if they are not seeing or recalling the relationship.
When students have completed the worksheet review student findings with the whole group. Explain the relationships to be certain all students have identified them correctly.
Be sure to write or post the relationships on the board as these will be used in the lesson.
30° - 60° -90°: 1:√3:2 (longest side is 2 times the length of the shortest side and the middle length [across from the 60°] is √3 times the shortest side)
45° - 45° - 90°: 1:1:√2 (the hypotenuse is √2 times the equal legs [isosceles triangle])
1. Open the PowerPoint-Unit Circle Quadrant Values. Students will find and record answers to the questions on each slide. First, ask students to find a radian measure that is equal to the degree measure of 30°.
2. Next, have the students use the relationship of the sides of special right triangles to find the lengths of the sides of the 30° - 60° - 90° triangle. Remind them that they are working with the Unit Circle, so we know that the radius is 1 unit. They should be able to find the horizontal and vertical sides of the triangle which will become the x- and y-values for the coordinate point. You will want to point out that the horizontal side will correspond to the Cosine value and the vertical side will correspond to the Sine value.
3. Repeat steps 1-2 for the second slide 45°.
4. Finally repeat steps 1-2 for the third slide 60°.
5. Next show students slide 4. This slide contains the points that they found in the first three slides. Explain that you only need to know the coordinates of the points in the first quadrant. Have students take notes as you show them that the remaining quadrants can be thought of as a reflection of points across either the x- or y-axis (depending on the quadrant). If necessary, draw attention to the fact that the point is always either 30°, 45° or 60° from the x-axis. Therefore, the sides will be the same as the sides of the triangles in the first quadrant. Also, point out that the angles' measurements can be found by either subtracting x from π, adding x to π or subtracting x from 2π.
6. Pair students together and pass out "I Have, Who Has?" cards. It may be necessary for some pairs to have more than one card. Instruct students to take their "I have" statement and be sure that they are able to identify the degree measure, the radian measure, and the coordinate points. If they have an angle in quadrants II, III or IV, they should also recognize the angle expressed as π-x, π+x or 2π-x.
7. After students have all needed information ask the pair of students who has the "Start Here" card to go first. They should be able to self check as the first group reading their "I Have" statement should also be the last group to answer the "Who Has?" question.
Ask students to sketch and fill in the first quadrant of the unit circle. (A free printable blank copy can be found here.) Next, have them fill in the other quadrants using the information from quadrant I.