Trigonometry with The Unit Circle Cited and Colored

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Trigonometry with The Unit Circle

Area of the Sector of a Circle

A=1/2 r2 θ

6 trigonometric functions

Rarely used: -cosecant θ=Hypotenuse/Opposite (reciprocal of sine) -secant θ=Hypotenuse/Adjacent (reciprocal of cosine) -cotangent θ=Adjacent/Opposite (reciprocal of tangent)

Most commonly used: -sine θ=Opposite/Hypotenuse -cosecant θ=Adjacent/Hypotenuse -tangent θ=Opposite/Adajacent

Exact Value vs Approximate Value

Example Exact value: √5 __ 5 Approximate value: .4472

Approximate Value A rounded decimal that is found on a calculator

Exact Value Simplified fractions that can include radicals

Types of Angles

Quadrantal Angle: an angle with its terminal side on the x-axis or y-axis

Picture citation: http://philschatz.com/algebra-trigonometry-book/resources/CNX_Precalc_Figure_05_01_018.jpg

Reference Angle: acute angles formed by the terminal side and the x-axis

Picture citation: http://images.tutorvista.com/cms/images/39/reference-angle.PNG

Coterminal Angles: Angles with the same initial and terminal sides

45 degrees is the coterminal angle of 405 degrees Picture citation: http://www.scienceforums.net/uploads/SAngle.JPG

Radians and Degrees

Picture citation: https://www.wyzant.com/resources/lessons/math/trigonometry/unit-circle/memorizing-coordinates

Radian: One radian is the measure of a central angle that intercepts an arc s equal in length to the radius r of the circle. Picture citation: https://www.varsitytutors.com/assets/vt-hotmath-legacy/hotmath_help/topics/radian-measure/radian-measure-image002.gif