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國立台灣大學九十學年度第二學期生物力學 REVIEW OF BASIC MATHEMATICS Plane Geometry 1. angles, sides, and area of a triangle 2. angles, sides, and area of a polygon 3. radius, diameter, circumference, and area of a circle 4. arc length and area of a sector of a circle Plane Trigonometry 1. define an angle between 2 lines 2. units used to measure angles 3. orthogonal projections of a line segment onto two perpendicular axes 4. define of sine (sin) 5. define of cosine (cos) 6. define of tangent (tan) 7. inverse trigonometric relationship: if sin = a 8. law of sine: then = sin-1 a a b c sin A sin B sin C 9. law of cosine: a 2 b 2 c 2 2bc cos A 10. solution of an arbitrary triangle a. knowing 3 sides to determine the angles b. knowing 2 sides and 1 angle to find the rest of the angles and sides c. knowing 2 angles and 1 side to find the rest of the angles and sides 11. area of an arbitrary triangle A 1 bc sin A 1 ab sin C 1 ca sin B 2 2 2 A s(s a)( s b)( s c) where s or abc 2 Vector 1. vector addition or subtraction 2. vector decomposition 3. expressed by unit vectors HC\BioMech\RevMath2.doc 1 Feb 22, 2001 國立台灣大學九十學年度第二學期生物力學 REVIEW OF BASIC MATHEMATICS magnitude point of application line of action sense HC\BioMech\RevMath2.doc 2 Feb 22, 2001