1. Math 20-1 Chapter 2 Trigonometry 2.1 A Angles in Standard Position Teacher Notes

2. Math 20-1 Chapter 1 Sequences and Series 2.1A Angles in Standard Position 2.1.1 In geometry, an angle is formed by two rays with a common endpoint. In trigonometry, angles may be interpreted as rotations of a ray. Vertex Initial Arm Terminal Arm

3. Angles in Standard Position Yes Examples No Examples Where would these go? NoYesNo How would you describe an angle in standard position? 2.1.2

4. Angles in Standard Position Initial armVertex Terminal arm x y An angle  is said to be in standard position if its vertex is at the origin of a rectangular coordinate system and its initial arm coincides with the positive x-axis. The rotation of angle  is measured in degrees. 2.1.3

5. Sketch each angle in standard position. State the quadrant in which the terminal arm lies. 50 ° 170 ° 200 ° 300 ° 2.1.4

6. Investigating Angles in Standard Position Create a 30°-60°-90° Triangle 3. For this activity, assume that the equilateral triangle has side lengths of 2 units. a) To obtain a 30°-60°-90° triangle, fold the triangle in half, as shown. b) Label the angles in the triangle as 30°, 60°,and 90°. 1. Begin with an 8 1/2 × 11 sheet of paper. Fold the paper in half lengthwise and make a crease down the middle. 2. Unfold the paper. In Figure 1, the corners are labelled A, B, C, and D. a) Take corner C to the centre fold line and make a crease, DE. See Figure 2. b) Fold corner B so that BE lies on the edge of segment DE. The fold will be along line segment CE. Fold the overlap (the grey-shaded region) under to complete the equilateral triangle (DEF). See Figure 3. 2.1.5

7. Reflections of Reference Angles 30 0 Angle in Standard Position_______ 30 0 Angle in Standard Position_______ 150 0 Angle in Standard Position_______ 210 0 Angle in Standard Position_______ 330 0 2.1.6

8. Reflections of Reference Angles 60 0 Angle in Standard Position _______ 60 0 Angle in Standard Position _______ 120 0 Angle in Standard Position _______ 240 0 Angle in Standard Position _______ 300 0 2.1.7

9. Reference Angles [Cont’d] Angle in Standard Position _______ 2.1.8

10. Sketching Angles in Standard Position Sketch the following angles in standard position. State the size of the reference angle. In which quadrant does the terminal arm lie? a) 150 0 b) 290 0 c) 215 0 Reference Angle 30 0 70 0 35 0 Quadrant II IV III 2.1.9

11. Drawing Angles in Standard Position Given a Point on the Terminal Arm Draw an angle, , in standard position such that the point P(-4, 3) lies on the terminal arm of an angle . P(-4, 3) -4 3  ref 2.1.10

12. Drawing Angles in Standard Position Given a Point on the Terminal Arm Suppose the point P(-4, 3) was reflected in the y-axis. 2.1.11 P(-4, 3)  37 0 Q(4, 3) 37 0 What the coordinates of the image point? What is the measure of the reference angle?

13. Drawing Angles in Standard Position Given a Point on the Terminal Arm Suppose the point P(-4, 3) was reflected in the y-axis. 2.1.12 P(-4, 3)  37 0 R(-4, -3) 37 0 What the coordinates of the image point? What is the measure of the reference angle?

14. Drawing Angles in Standard Position Given a Point on the Terminal Arm Suppose the point P(-4, 3) was reflected in the x-axis and y-axis. 2.1.10 P(-4, 3)  37 0 S(4, -3) 37 0 What the coordinates of the image point? What is the measure of the reference angle?

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