11X1 T08 03 angle between two lines (2010)

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<ul><li> 1. Angle Between Two Lines </li> <li> 2. Angle Between Two Lines y x </li> <li> 3. Angle Between Two Lines y 1 x l1 </li> <li> 4. Angle Between Two Lines y l1 has slope m1 tan 1 1 x l1 </li> <li> 5. Angle Between Two Lines l y 2 l1 has slope m1 tan 1 2 1 x l1 </li> <li> 6. Angle Between Two Lines l y 2 l1 has slope m1 tan 1 l2 has slope m2 tan 2 2 1 x l1 </li> <li> 7. Angle Between Two Lines l y 2 l1 has slope m1 tan 1 l2 has slope m2 tan 2 2 1 x l1 </li> <li> 8. Angle Between Two Lines l y 2 l1 has slope m1 tan 1 l2 has slope m2 tan 2 2 1 1 2 (exterior ) x l1 </li> <li> 9. Angle Between Two Lines l y 2 l1 has slope m1 tan 1 l2 has slope m2 tan 2 2 1 1 2 (exterior ) x 1 2 l1 </li> <li> 10. Angle Between Two Lines l y 2 l1 has slope m1 tan 1 l2 has slope m2 tan 2 2 1 1 2 (exterior ) x 1 2 tan tan 1 2 l1 </li> <li> 11. Angle Between Two Lines l y 2 l1 has slope m1 tan 1 l2 has slope m2 tan 2 2 1 1 2 (exterior ) x 1 2 tan tan 1 2 l1 tan 1 tan 2 1 tan 1 tan 2 </li> <li> 12. Angle Between Two Lines l y 2 l1 has slope m1 tan 1 l2 has slope m2 tan 2 2 1 1 2 (exterior ) x 1 2 tan tan 1 2 l1 tan 1 tan 2 1 tan 1 tan 2 m1 m2 1 m1m2 </li> <li> 13. Angle Between Two Lines l y 2 l1 has slope m1 tan 1 l2 has slope m2 tan 2 2 1 1 2 (exterior ) x 1 2 tan tan 1 2 l1 tan 1 tan 2 1 tan 1 tan 2 m1 m2 1 m1m2 The acute angle between two lines with slopes m1 and m2 can be found using; </li> <li> 14. Angle Between Two Lines l y 2 l1 has slope m1 tan 1 l2 has slope m2 tan 2 2 1 1 2 (exterior ) x 1 2 tan tan 1 2 l1 tan 1 tan 2 1 tan 1 tan 2 m1 m2 1 m1m2 The acute angle between two lines with slopes m1 and m2 can be found using; m1 m2 tan 1 m1m2 </li> <li> 15. 2000 Extension 1 HSC Q1b) e.g. Find the acute angle between the lines 1 y 2 x 1 and y x 1 3 </li> <li> 16. 2000 Extension 1 HSC Q1b) e.g. Find the acute angle between the lines 1 y 2 x 1 and y x 1 3 1 2 tan 3 1 1 2 3 </li> <li> 17. 2000 Extension 1 HSC Q1b) e.g. Find the acute angle between the lines 1 y 2 x 1 and y x 1 3 1 2 tan 3 1 1 2 3 6 1 3 2 </li> <li> 18. 2000 Extension 1 HSC Q1b) e.g. Find the acute angle between the lines 1 y 2 x 1 and y x 1 3 1 2 tan 3 1 1 2 3 6 1 3 2 1 </li> <li> 19. 2000 Extension 1 HSC Q1b) e.g. Find the acute angle between the lines 1 y 2 x 1 and y x 1 3 1 2 tan 3 1 1 2 3 6 1 3 2 1 45 </li> <li> 20. 2005 Extension 1 HSC Q1f) (ii) The acute angle between the lines y = 3x + 5 and y = mx + 4 is 45 Find the possible values of m. </li> <li> 21. 2005 Extension 1 HSC Q1f) (ii) The acute angle between the lines y = 3x + 5 and y = mx + 4 is 45 Find the possible values of m. 3 m tan 45 1 3m </li> <li> 22. 2005 Extension 1 HSC Q1f) (ii) The acute angle between the lines y = 3x + 5 and y = mx + 4 is 45 Find the possible values of m. 3 m tan 45 1 3m 3 m 1 1 3m </li> <li> 23. 2005 Extension 1 HSC Q1f) (ii) The acute angle between the lines y = 3x + 5 and y = mx + 4 is 45 Find the possible values of m. 3 m tan 45 1 3m 3 m 1 1 3m 1 3m 3 m </li> <li> 24. 2005 Extension 1 HSC Q1f) (ii) The acute angle between the lines y = 3x + 5 and y = mx + 4 is 45 Find the possible values of m. 3 m tan 45 1 3m 3 m 1 1 3m 1 3m 3 m 1 3m 3 m or 1 3m 3 m </li> <li> 25. 2005 Extension 1 HSC Q1f) (ii) The acute angle between the lines y = 3x + 5 and y = mx + 4 is 45 Find the possible values of m. 3 m tan 45 1 3m 3 m 1 1 3m 1 3m 3 m 1 3m 3 m or 1 3m 3 m 4m 2 </li> <li> 26. 2005 Extension 1 HSC Q1f) (ii) The acute angle between the lines y = 3x + 5 and y = mx + 4 is 45 Find the possible values of m. 3 m tan 45 1 3m 3 m 1 1 3m 1 3m 3 m 1 3m 3 m or 1 3m 3 m 4m 2 1 m 2 </li> <li> 27. 2005 Extension 1 HSC Q1f) (ii) The acute angle between the lines y = 3x + 5 and y = mx + 4 is 45 Find the possible values of m. 3 m tan 45 1 3m 3 m 1 1 3m 1 3m 3 m 1 3m 3 m or 1 3m 3 m 4m 2 1 3m 3 m 1 m 2 </li> <li> 28. 2005 Extension 1 HSC Q1f) (ii) The acute angle between the lines y = 3x + 5 and y = mx + 4 is 45 Find the possible values of m. 3 m tan 45 1 3m 3 m 1 1 3m 1 3m 3 m 1 3m 3 m or 1 3m 3 m 4m 2 1 3m 3 m 1 m 2m 4 2 </li> <li> 29. 2005 Extension 1 HSC Q1f) (ii) The acute angle between the lines y = 3x + 5 and y = mx + 4 is 45 Find the possible values of m. 3 m tan 45 1 3m 3 m 1 1 3m...</li></ul>