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Page 857

Page 857. Evaluating Trig Functions of Any Angle. Section 13.3. 5. 4. 3. Review. Determine the Trigonometric Functions for Ѳ. SIN ө = COS ө = TAN ө = CSC ө = SEC ө = COT ө =. Equation in Standard Form.

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Page 857

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  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

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