Unit circle, intro to circular functions
- 1. THE UNIT CIRCLE by: SHIRLY M. MASANGKAY,Ed.D. Occidental Mindoro National High School Mamburao, Occidental Mindoro
- 2. REVIEW
- 3. REFERENCE ANGLE - an angle whose measure is less than 900 which is found between the terminal side and the x-axis from an angle in standard position. 300 450 600 900 1200 1350 1500 1800 2100 2250 3300 3000 2400 2700 3150 3600 00
- 5. (1,0) (0, -1) (0, 1) (-1, 0) P (x,y) r x y O-1 -1 1 1 by Pythagorean Theorem: OP2 = OM2 +PM2 or 12 = x2 + y2 x2 + y2 = 1 The equation of the circle with center at (0,0) and radius 1. θ M
- 8. 2Π450 450 4 ∏ 4 3∏ 2 ∏ 4 5∏ 4 7 ∏ 2 3∏ Π for 45 degrees angle 900 v
- 11. COORDINATES OF POINTS ON THE UNIT CIRCLE 300 450 600 900 1200 1350 1500 1800 2100 2250 3300 3000 2400 2700 3150 3600 00 2 1 , 2 3 4 ∏ − 2 1 , 2 3 −− 2 1 , 2 3 − 2 1 , 2 3 6 5∏ 6 7∏ 6 11∏ 6 ∏ 2 2 , 2 2 − 2 2 , 2 2 −− 2 2 , 2 2 − 2 2 , 2 2 4 3∏ 4 5∏ 4 7∏ 3 ∏ 2 3 , 2 1 − 2 3 , 2 1 −− 2 3 , 2 1 3 2∏ 3 4∏ − 2 3 , 2 1 3 5∏ 2Π (1,0) (0,1) 2 ∏ (-1,0) Π 2 3∏ (0,-1)
- 12. Activity No. 1: Label the unit circle using the 30-45-60-degree scales and its corresponding radian measures.
- 13. Activity No. 2: Label the unit circle using the 30-45-60-degree scales and its corresponding radian measures and coordinates.
- 14. Activity No. 3 A. Find the equivalent radian measure of the following degree measures. 1. 300 ____________________________ 2. 22.50 ____________________________ 3. 1200 ____________________________ 4. 3900 ____________________________ 5. 4800 ____________________________ 6. 4050 ____________________________ 7. 4200 ____________________________ 8. 900 ____________________________ 9. 6300 ____________________________ 10. 2400 ____________________________ B. Find the equivalent degree measure of the following radian measures. 1. ___________ 6. ___________ 2. ___________ 7. ___________ 3. ___________ 8. ___________ 4. ___________ 9. ___________ 5. ___________ 10. ___________ 3 ∏ 3 4∏ 4 3∏ 6 5∏ 6 7∏ ∏7 2 5∏ 2 3∏ 4 7 ∏ 6 7∏
- 15. Activity No.4 COORDINATES OF POINTS ON THE UNIT CIRCLE Direction: Find the other coordinate of the point of intersection P of the unit circle. The terminal side of an agle is given. Write the corresponding letter/symbol of the correct answer in the boxes below. ---- x = S y = T y = N y = L x = E x = A y = W y = R x = I x = What relation to you is your brother's son's sister's mother? 3 2 4 3 7 2 4 1 6 5 5 3 3 1 11 6 8 5 5 4 4 7 5 10 4 7 7 53 11 85 5 4 3 5 5 10 3 22 3 5 4 15 6 11 8 39