Modeling with Trigonometric Functions and Circle Characteristics Unit 8.

Unit 9

Modeling with Trigonometric Functions and Circle CharacteristicsUnit 8Trig. Stuff

Special Right Triangles

30-60-9045-45-9030-60-90This is half of an equilateral triangleThe hypotenuse = short leg times 2The long leg = short leg times 345-45-90This comes from half of a squareThe legs are equalHypotenuse = leg times 2Leg = the hypotenuse times 2The Unit Circle

Convert from degrees to radianConvert from radian to degreesHow 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-) + 4What is the amplitude?3 How do I find the period of a trig. Function?Trig. IdentitiesStuff about circles!

TheoremRadius to a tangent: Right angle

If a radius is drawn to a tangent, then the radius is perpendicular to the tangent.

TheoremCongruent chords are equidistant from the center of the circle.

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

Hat TheoremIf two tangents are drawn to a circle from an exterior point, then the tangent segments are congruent.

Equation of a circleDistance FormulaMidpoint FormulaLength of an arc =

Area of a sector=

Central Angle =Same as the arc

Inscribed Angle = the arc

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

Angle outside the circle = the difference of the arcs

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

Area of an equilateral triangle