1. Modeling with Trigonometric Functions and Circle Characteristics Unit 8

2. Trig. Stuff

3. Special Right Triangles 30-60-90 45-45-90

4. 30-60-90 This is half of an equilateral triangle The hypotenuse = short leg times 2 The long leg = short leg times √3

5. 45-45-90 This comes from half of a square The legs are equal Hypotenuse = leg times √2 Leg = ½ the hypotenuse times √2

6. The Unit Circle

7. Convert from degrees to radian

8. Convert from radian to degrees

9. How do I find the amplitude of a trig. Function? The amplitude equals the absolute value of a. a is located in front of the trig. function Example: f(x) = -3cos(x- π ) + 4 What is the amplitude? 3

10. How do I find the period of a trig. Function?

11. Trig. Identities

12. Stuff about circles!

13. Theorem Radius to a tangent: Right angle If a radius is drawn to a tangent, then the radius is perpendicular to the tangent.

14. Theorem Congruent chords are equidistant from the center of the circle.

15. Theorem If a radius is perpendicular to a chord, then it bisects the chord and its arcs.

16. “Hat Theorem” If two tangents are drawn to a circle from an exterior point, then the tangent segments are congruent.

17. Equation of a circle

18. Distance Formula

19. Midpoint Formula

20. Length of an arc =

21. Area of a sector=

22. Central Angle = Same as the arc

23. Inscribed Angle = ½ the arc

24. Angle inside the circle formed by two chords = ½ the sum of the arcs

25. Angle outside the circle = ½ the difference of the arcs

26. What do you know about a quadrilateral inscribed in a circle? It’s opposite angles are supplementary (they have a sum of 180º).

27. Area of an equilateral triangle