初中数学三角行汇总(国外英语资料).docVIP

初中数学三角行汇总(国外英语资料) Form: theorem, proof, inference, problem. (1) trigonometric function correlation: 1. sine theorem 3L 2. cosine theorem 4L 3. - point theorem and angular bisector theorem 5L 4. times / half angle formula 6L 5. trigonometric function and area formula 7L (2) triangle four heart correlation 6. out of 8L 7. inner 9L 8. center of gravity 10L 9. altitudes of 11L 10. Euler theorem (Euler) 12L The 11. circle associated with the circumcircle radius formula of 13L The 12. formula 14L Orthocentre 2011-08-10 21:13 | reply Report Free flight 540893238 trumpet Core member 6 The 3 floor Sine theorem: Delta ABC, AB/sinc=BC/sinA=CA/sinB=2R (R ABC circumradius) Proof: A AH group of BC, namely AH=AB*sinB=AC*sinC, AB/sinC=AC/sinB, gained AB/sinc=BC/sinA=CA/sinB, about the value of 2R, will be in 13L (inscribed circle associated with the radius of circumcircle formula) in detail Corollary: the greater the sin value in a triangle, the greater the relative edge (relative to the other side). Exercises: 1. in ABC, AB=5 / B=30 / C=45 degrees, AC. degrees. By AB/sinc=CA/sinB 5/sin45 ~ =AC/sin30 ~ AC= (5 V 2) /2 2011-08-10 21:44 | reply Report Free flight 540893238 trumpet Core member 6 The 4 floor The cosine theorem: for any triangle, cosC= (a^2+b^2-c^2), /2ab, cosB= (a^2+c^2-b^2), /2ac, cosA= (c^2+b^2-a^2) /2bc. Proof: AD BC / C group, on the edge of the C / B on the edge of B / A on the edge of a, there are BD=cosB*c, AD=sinB*c, DC=BC-BD=a-cosB*c, by the Pythagorean theorem can be AC^2=AD^2+DC^2, b^2= (sinB*c) ^2+ (a-cosB*c) ^2=sinB^2*c^2+a^2+cosB^2*c^2-2ac*cosB= (sinB^2+cos^2) c^2+a^2-2ac*cosB=a^2+c^2-2ac*cosB. There are cosB= (a^2+c^2-b^2) /2ac, cosC= (a^2+b^2-c^2) in /2ab, cosA= (c^2+b^2-a^2) /2bc. Corollary: the condition of a triangle: one corner, two sides, two corners, one side (with the triangle side), and the three side. Exercises: in ABC, if a*sinA+b*sinB=c*sinC, triangle shape: Solution: =a by cosine theorem (c^2+b^2-a^2) /2bc+b (a^2+c^2-b^2) /2ac=c (a^2+b^2-c^2