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CW#69H: Trig of All Angles Honors Geometry Teacher Notes – KEY CRS FUN 703 - Exhibit knowledge of unit circle trigonometry. Objective 10.15B - Evaluate the 6 trigonometric functions of any angle using reference angles. Review: If is not a quadrantal angle, the sign of a trig function depends on the quadrant in which lies: Draw Picture: *A way for students to remember is the saying: “A Smart Trig Class” or “All Students Take Calculus” ASTC *All positive in Q1 *Sine (and reciprocal function cosecant) positive in Q2 *Tangent (and reciprocal cotangent) positive in Q3 *Cosine (and reciprocal secant) positive in Q4 Example 1: If tan 0 and cos 0, name the quadrant in which lies. Unit circle w/ radius r *y will always be the side opposite *x will always be the side adjacent *the hypotenuse is the radius, r Ex 2. Let (8, -10) be a point on the terminal side of an angle in standard position. Find the exact value of each of the six trig functions of . CW#69H: Trig of All Angles Honors Geometry Classroom Copy –DO NOT WRITE ON! CRS FUN 703 - Exhibit knowledge of unit circle trigonometry. Objective 10.15B - Evaluate the 6 trigonometric functions of any angle using reference angles. Directions: A point on the terminal side of an angle θ is given. Find the exact value of sec, csc, and cot. 1. (-3,4) 2. (5,-12) 3. (2, -3) 4. (-1, -2) 5. (-3,-3) 6. (2, -2) Directions: Use reference angles to find the exact value of each expression. WATCH YOUR SIGNS! 7. sin 510⁰ 8. cos 600⁰ 9. cot 330⁰ 10. sin 3 4 11. tan (7π) 12. csc 300⁰ 13. Find the exact value: do NOT use a calculator. 14. Find the exact value: cos 540⁰ tan ( 405⁰) sin 270ᵒ + cos(-180ᵒ) 15. Find the exact value: 16. Find the exact value: tan π + sin π 6cos ( 3 ) + 2tan ( ) 4 3 17. Review: Find the three smallest positive angles coterminal to -800°. 18. Review: Find the three smallest positive angles coterminal to 6413°. 19. Review: Given the following triangle, find the remaining sides. 20. Review: Given the following triangle, find the missing angles and side. 26 r 10 y M 40ᵒ x 33 Q