Unit 8 Modeling with Trigonometric Functions and Circle

Unit 8 Modeling with Trigonometric Functions and Circle Characteristics

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

Convert from degrees to radian �

Convert from radian to degrees �

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) = -3 cos(x-π) + 4 What is the amplitude? 3

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

Trig. Identities �

Stuff about circles! �

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 �