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Published byClaude Logan Modified over 8 years ago

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Modeling with Trigonometric Functions and Circle Characteristics Unit 8

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Trig. Stuff

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

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

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

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The Unit Circle

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Convert from degrees to radian

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Convert from radian to degrees

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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

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

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Trig. Identities

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Stuff about circles!

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

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

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

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

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Equation of a circle

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Distance Formula

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Midpoint Formula

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Length of an arc =

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Area of a sector=

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Central Angle = Same as the arc

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Inscribed Angle = ½ the arc

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

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Angle outside the circle = ½ the difference of the arcs

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

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Area of an equilateral triangle

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