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Introduction to Trigonometric Functions

Explore trigonometry, angles, and the unit circle in this honors precalculus introduction. Learn to evaluate trigonometric functions and convert angles between degrees and radians.

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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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