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Introduction to Trigonometric Functions

Introduction to Trigonometric Functions. Honors Precalculus November 8-9, 2016 Mrs. Agnew. Essential Question What is the Unit Circle and how do we use it to evaluate trigonometric functions? Essential Vocabulary Unit Circle Degrees Radians Trigonometric Functions. The Unit Circle.

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Introduction to Trigonometric Functions

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  1. Introduction to Trigonometric Functions Honors Precalculus November 8-9, 2016 Mrs. Agnew

  2. Essential Question • What is the Unit Circle and how do we use it to evaluate trigonometric functions? Essential Vocabulary • Unit Circle • Degrees • Radians • Trigonometric Functions

  3. The Unit Circle • The Unit Circle is a circle centered at the origin with radius of 1. • All of trigonometry is based on the unit circle. • Trigonometry is the study of angles and the corresponding points on the unit circle.

  4. Angles • Angle in standard position • One side on positive x axis and vertex at origin • Angles can be positive or negative, and can be larger than 180°. • Angles can be measured in degrees or in radians.

  5. Converting Angles • Angles can be measured in degrees or radians. • To convert an angle… From Degrees to Radians: From Radians to Degrees:

  6. All angles have a reference angle in the first quadrant. Coterminal angles… all angles have a coterminal angle between 0° and 360° OR 0 and 2π Reference Angles Examples…

  7. The Unit Circle • We are going to fill in values on our unit circle. • “Special Angles” on the unit circle • 30, 60, 90 and 45, 45, 90 • “Special Angles” on unit circle give “special points” on the unit circle.

  8. Given a point (x,y) on the unit circle, the value of the 6 trig functions are… sinθ = y cosθ = x tanθ = y/x cscθ = 1/y secθ = 1/x cotθ = x/y (reciprocal of y) (reciprocal of x) Evaluating Trig Functions

  9. Evaluating Trig Functions When evaluating a trig function… • Find coterminal angle on unit circle • Determine sign of value (All Students Take Calculus) • Find reference angle • Find value Examples, on & off calc

  10. Homework: Evaluating Trig Worksheet

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