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NAME DATE 12-3 PERIOD Practice Trigonometric Functions of General Angles The terminal side of θ in standard position contains each point. Find the exact values of the six trigonometric functions of θ. 1. (6, 8) 3 4 sin θ = − , cos θ = − , 2 √ 29 29 20 21 sin θ = − , cos θ = - − , 5 5 5 4 tan θ = − , csc θ = − , 3 4 5 3 sec θ = − , cot θ = − 3 4 5 √ 29 29 3. (-2, -5) sin θ = - − , 2. (-20, 21) 29 21 tan θ = - − , csc θ = 20 29 sec θ = - − , cot θ = 20 cos θ = - − , 29 29 , − 21 20 -− 21 √ 29 5 tan θ = − , csc θ = - − , 5 √ 29 2 sec θ = - − , cot θ = − 5 2 2 Sketch each angle. Then find its reference angle. 3π − 13π 4. − 8 5. -210° 8 7π 6. - − 30° 4 π − 4 y y y 13π 8 θ° θ° O x O O x θ° x - 7π 4 -210° Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Find the exact value of each trigonometric function. 7. tan 135° -1 8. cot 210° 5π 3 - √ 11. tan − 3π 12. csc - − 3 ( 4 √ 3 ) 9. cot (-90°) 0 √2 2 √3 − 3 10. cos 405° − 13π 2 13. cot 2π undefined 14. tan − - √ 6 15. LIGHT Light rays that “bounce off ” a surface are reflected by the surface. If the surface is partially transparent, some of the light rays are bent or refracted as they pass from the air through the material. The angles of reflection θ1 and of refraction θ2 in the diagram at the right are related by the , find the equation sin θ1 = n sin θ2. If θ1 = 60° and n = √3 measure of θ2. 30° air θ1 θ1 surface θ2 800 N 16. FORCE A cable running from the top of a utility pole to the ground exerts a horizontal pull of 800 Newtons and a vertical 3 Newtons. What is the sine of the angle θ between the pull of 800 √ cable and the ground? What is the measure of this angle? 800 3N √3 2 −; 60° Chapter 12 20 Glencoe Algebra 2