Trigonometric Functions of Any Angle Section 9 3

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Trigonometric Functions of Any Angle Section 9. 3 – Part 2 1

Trigonometric Functions of Any Angle Section 9. 3 – Part 2 1

What You Will Learn Evaluate trigonometric functions of any angle. Find and use reference

What You Will Learn Evaluate trigonometric functions of any angle. Find and use reference angles to evaluate trigonometric functions 2

Take Note 3

Take Note 3

Reference angle Let θ be an angle in standard position. Its reference angle is

Reference angle Let θ be an angle in standard position. Its reference angle is the acute angle θ‘ formed by the terminal side of θ and the horizontal axis. 4

Take Note 5

Take Note 5

Reference angles are always measured between the x axis and the terminal side

Reference angles are always measured between the x axis and the terminal side of the angle (always +ves !) Notice the butterfly shape 6

Finding Reference Angles Example 3 Video 7 https: //static. bigideasmath. com/protected/content/hs_tut/alg 2/c 09/03/HSCC_Alg 2_09_03_ee

Finding Reference Angles Example 3 Video 7 https: //static. bigideasmath. com/protected/content/hs_tut/alg 2/c 09/03/HSCC_Alg 2_09_03_ee 3. html

Drawing Reference Angles Find the reference angle θ', and sketch θ and θ' in

Drawing Reference Angles Find the reference angle θ', and sketch θ and θ' in standard position. 1) θ = -145° 2) 8

Drawing Reference Angles Find the reference angle θ', and sketch θ and θ' in

Drawing Reference Angles Find the reference angle θ', and sketch θ and θ' in standard position. 1) θ = -130° 9

Using reference angles to Evaluate Functions 1. Find the reference angle 2. Determine the

Using reference angles to Evaluate Functions 1. Find the reference angle 2. Determine the value of the given trig function of the reference angle. 3. Determine the sign—based on the quadrant of the given (original) angle 10

Using Reference Angles to Evaluate Functions Evaluate (a) tan(− 240º) and (b) csc 17π/6.

Using Reference Angles to Evaluate Functions Evaluate (a) tan(− 240º) and (b) csc 17π/6. Example 4 Video 11 https: //static. bigideasmath. com/protected/content/hs_tut/alg 2/c 09/03/HSCC_Alg 2_09_03_ee 4. html

More Examples Video 5: https: //static. bigideasmath. com/protected/content/hs_tut/alg 2/c 09/03/HSCC_Alg 2_09_03_mp 5. html Video

More Examples Video 5: https: //static. bigideasmath. com/protected/content/hs_tut/alg 2/c 09/03/HSCC_Alg 2_09_03_mp 5. html Video 6: https: //static. bigideasmath. com/protected/content/hs_tut/alg 2/c 09/03/HSCC_Alg 2_09_03_mp 6. html Video 7: https: //static. bigideasmath. com/protected/content/hs_tut/alg 2/c 09/03/HSCC_Alg 2_09_03_mp 7. html Video 8: https: //static. bigideasmath. com/protected/content/hs_tut/alg 2/c 09/03/HSCC_Alg 2_09_03_mp 8. html Video 9: Video 10: Video 11: https: //static. bigideasmath. com/protected/content/hs_tut/alg 2/c 09/03/HSCC_Alg 2_09_03_mp 10. html 12 Example 5 Video: https: //static. bigideasmath. com/protected/content/hs_tut/alg 2/c 09/03/HSCC_Alg 2_09_03_ee 5. html https: //static. bigideasmath. com/protected/content/hs_tut/alg 2/c 09/03/HSCC_Alg 2_09_03_mp 9. html https: //static. bigideasmath. com/protected/content/hs_tut/alg 2/c 09/03/HSCC_Alg 2_09_03_mp 10. html