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Chapter 13 Section 2

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Chapter 13 Section 2. Angles and the Unit circle. Parts of an angle. Terminal Side. Vertex. Initial Side. Standard Position. Vertex is at the center Initial side is on the + x axis. 70 0. Standard Position. If terminal ray is in the II quadrant. 30 0. Standard Position.

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Chapter 13 Section 2

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  1. Chapter 13 Section 2 Angles and the Unit circle

  2. Parts of an angle Terminal Side Vertex Initial Side

  3. Standard Position • Vertex is at the center • Initial side is on the + x axis 700

  4. Standard Position • If terminal ray is in the II quadrant 300

  5. Standard Position • If terminal side is in the III quadrant 200

  6. Standard Position • If terminal side is in the IV quadrant 400

  7. Find the measure of each angle 110 150 450

  8. Negative Angle • If you measure an angle counter clockwise you call can give the angle a negative degree -400

  9. Co-Terminal measures • A negative angle and + angle measure that describe the same angle are called Co- Terminal -400 and 320o are co-terminal

  10. Find the Co Terminal Angle • -350 • -2000 • -3000 • -2820 • 1850 • 3300

  11. Unit Circle • A Circle with a radius of one unit centered on the origin (1,0) 1 unit

  12. Unit Circle For angles in standard position we use the variable q to show we are talking about an angle ( q (1,0) 1 unit

  13. For any point on the unit circle, we can find the coordinates by using the angle in standard position and the rule (cos(q) , sin(q)) (cos(300) , sin(300)) 300 (1,0) 1 unit

  14. Cosine and Sine of 30-60-90 triangles Sin (30) Cos (30) 2 1

  15. Cosine and Sine of 30-60-90 triangles Sin (60) Cos (60) 2 1 300

  16. Cosine and Sine of 45-45-90 triangles Sin (45) Cos (45) 1 450 1

  17. Make a 30-60-90 triangle and look at the coordinates For angles with a terminal side not in the 1st quadrant (- , ) 1200 (1,0) 1 unit

  18. For angles with a terminal side not in the 1st quadrant use the rule QI (+,+) QII (-,+) QIII (-,-) QIV(+,-) Make a 30-60-90 triangle and look at the coordinates 2100 (1,0) 1 unit (- ,- )

  19. U Try For angles with a terminal side not in the 1st quadrant use the rule QI (+,+) QII (-,+) QIII (-,-) QIV(+,-) 3000 (1,0) 1 unit ( ,- )

  20. Do Now • Page 708 2 - 50

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