1 / 17

Mastering Trigonometric Functions: Evaluation & Examples

Learn to evaluate trigonometric functions for any angle, establish radius, and find reference angles with helpful examples and step-by-step instructions.

erinbarnes
Download Presentation

Mastering Trigonometric Functions: Evaluation & Examples

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Page 857 13.2 - Define General Angles and Radian Measure

  2. Evaluating Trig Functions of Any Angle Section 13.3 13.3 - Evaluating Trig Functions

  3. 5 4 3 Review • Determine the Trigonometric Functions for Ѳ SIN ө= COS ө = TAN ө = CSC ө = SEC ө = COT ө= 13.3 - Evaluating Trig Functions

  4. Equation in Standard Form • For ө be an angle in standard position with any point (x, y) • SIN ө = y/r • COS ө = x/r • TAN ө = y/x • CSC ө = r/y • SEC ө = r/x • COT ө = x/y B. To establish the radius, the equation is C. Think of “ASTC: All Students Take Calculus” • A: All points are always positive in Quadrant I • S: Sine points are positive in Quadrant II • T: Tan points are positive in Quadrant III • C: Cosine points are positive in Quadrant IV 13.3 - Evaluating Trig Functions

  5. Equation in Standard Form For ө be an angle in standard position with any point (x, y)… S A When ALL trig functions are positive When SIN is positive Quadrant II (– , +) Quadrant I (+, +) C T When TAN is positive When COS is positive Quadrant III (–, –) Quadrant IV (+, –) “All Students Take Calculus” 13-2 - Angles of Rotation

  6. Steps in Evaluating Functions given a Point • Draw a picture from a coordinate plane • Identify and plot the point onto the coordinate plane • Determine the missing side using the radius equation • Use Trigonometric Functions to solve 13.3 - Evaluating Trig Functions

  7. Example 1 • Let (3, 4) be a point on the terminal side of ө. Determine the value of the six trigonometric functions for ө. 4 3 13.3 - Evaluating Trig Functions

  8. Example 1 • Let (3, 4) be a point on the terminal side of ө. Determine the value of the six trigonometric functions for ө. 5 4 SIN ө = COS ө = TAN ө = CSC ө = SEC ө = COT ө = 3 13.3 - Evaluating Trig Functions

  9. Example 2 • Let (–3, 4) be a point on the terminal side of ө. Determine the value of the six trigonometric functions for ө. SIN ө = COS ө = TAN ө = CSC ө = SEC ө = COT ө = 13.3 - Evaluating Trig Functions

  10. Your Turn • Let (1, –1) be a point on the terminal side of ө. Determine the value of the six trigonometric functions for ө. SIN ө = COS ө = TAN ө = CSC ө = SEC ө = COT ө = 13.3 - Evaluating Trig Functions

  11. Reference Angles • Reference angles is a positive acute angle formed by the terminal side of ө and the x-axis. They are viewed as linear pairs. (Think: REFER’s back to the x-axis) • No reference trigonometric values of measure are greater than or equal to 90° or less than or equal to 0° 13.3 - Evaluating Trig Functions

  12. Reference Angles 13.3 - Evaluating Trig Functions

  13. Example 3 • Given Ѳ = 135°, determine the reference angle for each given angle. 135° 45° 13.3 - Evaluating Trig Functions

  14. Example 4 • Given Ѳ = –105°, determine the reference angle for each given angle. 13.3 - Evaluating Trig Functions

  15. Example 5 • Given Ѳ = 88°, determine the reference angle for each given angle. 13.3 - Evaluating Trig Functions

  16. Your Turn • Given Ѳ = 212°, determine the reference angle for each given angle. 13.3 - Evaluating Trig Functions

  17. Assignment • Page 870 • 3-15 odd, 16-23 all 13.3 - Evaluating Trig Functions

More Related