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Trigonometry

Trigonometry. θ. Definition of an angle. Terminal Ray. + Counter clockwise. Initial Ray. - clockwise. Terminal Ray. Radian Measure. Definition of Radians. C= 2 π r. C= 2 π radii. C= 2 π radians. 360 o = 2 π radians. r. 180 o = π radians. 1 Radian  57.3 o. r.

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Trigonometry

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  1. Trigonometry θ

  2. Definition of an angle Terminal Ray + Counter clockwise Initial Ray -clockwise Terminal Ray

  3. Radian Measure

  4. Definition of Radians C= 2πr C= 2π radii C= 2π radians 360o = 2πradians r 180o = π radians 1 Radian  57.3 o r

  5. Unit Circle – Radian Measure

  6. Unit Circle – Radian Measure

  7. Unit Circle – Radian Measure Degrees

  8. Converting Degrees ↔ Radians Converts degrees to Radians Recall Converts Radians to degrees more examples

  9. Coterminal angles – angles with a common terminal ray Terminal Ray Initial Ray

  10. Coterminal angles – angles with a common terminal ray Terminal Ray Initial Ray

  11. Trigonometric Ratios

  12. Basic ratio definitions Hypotenuse Opposite Leg Reference Angle θ Adjacent Leg

  13. Circle Trigonometry Definitions (x, y) Radius = r Opposite Leg = y Adjacent Leg = x reciprocal functions

  14. Unit - Circle Trigonometry Definitions (x, y) Radius = 1 Opposite Leg = y Adjacent Leg = x 1

  15. Unit Circle – Trig Ratios sin cos tan (+, +) (-, +) (+, -) (-, -) Skip π/4’s Reference Angles

  16. Unit Circle – Trig Ratios sin cos tan (-, +) (+, +) (-, -) (+, -)

  17. Unit Circle – Trig Ratios sin cos tan (-, +) (+, +) (0 , 1) Quadrant Angles (-1, 0) (1, 0) sin cos tan 0 /2π 0 1 0 0 Ø 1 (0, -1) (-, -) (+, -) 0 0 -1 Ø -1 0 View π/4’s

  18. Unit Circle – Radian Measure sin cos tan (-, +) (+, +) Quadrant Angles sin cos tan 1 0 /2π 0 1 0 0 Ø 1 (-, -) (+, -) 0 0 -1 Ø Degrees -1 0

  19. A unit circle is a circle with a radius of 1 unit. For every point P(x, y) on the unit circle, the value of r is 1. Therefore, for an angle θin the standard position:

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