# Modeling with Trigonometric Functions and Circle Characteristics Unit 8.

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Modeling with Trigonometric Functions and Circle Characteristics Unit 8

Trig. Stuff

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

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

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

The Unit Circle

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

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

Trig. Identities

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

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

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

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

Equation of a circle

Distance Formula

Midpoint Formula

Length of an arc =

Area of a sector=

Central Angle = Same as the arc

Inscribed Angle = ½ the arc

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

Angle outside the circle = ½ the difference of the arcs

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

Area of an equilateral triangle