Pre-Calculus: Angle Operations Identities

Eyles’ Pre-calculus ANGLE OPERATIONS IDENTITIES 1. Assume that cos(a - ß) = cosa cosß + sina sinß BONUS: Prove the following identities. ( HINT S ) 2. cos(90? - ß) = sinß apply#1 3. sin(90? - ß) = cosß ß = 90? - (90? - ß) 4. cos(-ß) = cosß - ß = 0? - ß 5. sin(-ß) = -sinß apply#2 6. cos(a + ß) = cosa cosß - sina sinß apply#1 then #5 7. sin(a + ß) = sina cosß + cosa sinß apply#2 then #1 then #3 8. sin(a - ß) = sina cosß - cosa sinß apply#7 then #2 then #3 9. sin 2ß = 2sinß cosß apply#7 10. cos 2ß = cos2ß - sin2ß apply#6 11. cos 2ß = 2cos2ß - 1 apply#10 12. cos 2ß = 1 - 2sin2ß apply#10 13. sin a 2 = ± s 1 - cosa 2 apply#12 14. cos a 2 = ± s 1 + cosa 2 apply#11 15. Derive Angle Operations Identity # 1 above using the distance formula. Eyles’ Pre-calculus ANGLE OPERATIONS PRACTICE PROBLEMS Apply the Angle Operations Identities on the previous page to Find the EXACT values. 16. a) cos(15? ) = b) sin(105? ) c) sin(-75? ) 17. a) cos( 11p 12 ) = b) sin( -13p 12 ) c) sin( -p 8 ) 18. a) cos(35? )cos(5? ) + sin(35? )sin(5? ) b) cos(95? )cos(55? ) - sin(95? )sin(55? ) 19. a) cos(143? )cos(83? ) + sin(143? )sin(83? ) b) cos(177? )cos(33? ) - sin(177? )sin(33? ) 20. a) sin(35? )cos(10? ) + cos(35? )sin(10? ) b) sin(950? )cos(650? ) - cos(950? )sin(650? ) 21. a) sin(143? )cos(37? ) + cos(143? )sin(37? ) b) sin(177? )cos(27? ) - cos(177? )sin(27? ) 22. a) cos(22.5 ? ) = b) sin(-67.5 ? ) c) sin(112.5 ? ) 23. a) cos( -p 12 ) = b) sin( -p 8 ) c) sin( -3p 8 ) If A B are in quadrant I and sinA = 2 5 and sinB = 10 11 find 24. a) cos(A + B) b) cos(A - B) 25. a) sin(A + B) b) sin(A - B) 26. a) cos(2A) b) sin(2A) 27. a) cos( A 2 ) b) sin( A 2 ) 2