Coordinate Geometry

Size: px

Start display at page:

Download "Coordinate Geometry"

伐乌孙
4 years ago
Views:

1 Coordinate Geometry 解析几何 Midpoint on a Coordinate Plane 平面中点公式 Midpoint on a Numer Line 线段中点公式 Midpoint in Spae 空间中点公式 Distane on a Coordinate Plane 平面距离公式 Distane on a Numer Line M = ( M = a + x + x, M = ( x + x y + y ), y + y, z + z ) d = (x - x ) + (y - y ) d = a - 线段距离公式 Distane in Spae 空间距离公式 d = (x - x ) + (y - y ) + (z - z ) Ar Length 曲线长度公式 Slope 斜率公式 Slope-Interept Form of a line 直线斜截式方程 Point-Slope Form of a line 直线点斜式方程 Equation for a Cirle on a Coordinate Plane 平面圆形方程 l = N 360 πr m = y - y x - x y = mx + y - y = m(x - x ) (x - h) + (y - k) = r Matries 矩阵 Matrix Multipliation 矩阵乘法 a a y = x y ax + x ay + y ax x ay y + + x Polynomials 多项式 Quadrati Formula 二次公式 x = Differene of Two Squares 平方差 Perfet square trinomials 完全平方三项式 ± 4a a a - = (a + )(a - ) a + a + = (a + ) a - a + = (a - )

2 Logarithms 对数 Proaility and Statistis 概率和统计 Change of Base Formula 基变换公式 Permutations 拓扑结构 Cominations 组合数学 log a n = log n log a (, ) P n r (, ) C n r n!! = ( n r) n!!! r = ( n r) Trigonometry 三角学 Standard Deviation 标准偏差 ( x - x) + ( x - x) + L + ( xn - x) Pythagorean Theorem 毕达哥拉斯定理 Law of Sines 正弦定理 Law of Cosines 余弦定理 Trigonometri Funtions 三角函数 Quotient Identities 三角恒等式 σ = a + = sin A sin B sin C = = a a = + os A sin θ = opp hyp s θ = hyp opp tan θ = sin θ os θ n os θ = adj hyp se θ = hyp adj ot θ = os θ sin θ tan θ = opp adj ot θ = adj opp Algerai Properties 代数性质 Reiproal Identities 倒数恒等式 Pythagorean Identities 毕达哥拉斯恒等式 Additive Identity 加法恒等式 Multipliative Identity 乘法恒等式 Sustitution (=) 代入律 (=) Reflexive (=) 自反律 (=) Symmetri (=) 对称律 (=) Transitive (=) 传递律 (=) s θ = se θ = ot θ = sin θ os θ tan θ os θ + sin θ = tan θ + = se θ ot θ + = s θ For any numer a, a + 0 = 0 + a = a. 对于任意数字 a, a + 0 = 0 + a = a. For any numer a, a = a = a. 对于任意数字 a, a = a = a. If a =, then a may e replaed y. 如果 a=, 则可以用来替代 a. a = a If a =, then = a. 如果 a =, 那么 = a. If a = and =, then a =. 如果 a = 且 =, 那么 a =.

3 Commutative (+) 互换律 (+) Commutative ( ) 互换律 ( ) Assoiative (+) 结合律 (+) Assoiative ( ) 结合律 ( ) Distriutive 分配律 Additive Inverse 加法逆元 Multipliative Inverse 乘法逆元 Multipliative (0) 乘法 (0) Addition (=) 加法 (=) Sutration (=) 减法 (=) Division and Multipliation (=) 除法和乘法 (=) Addition (>) 加法 (>) Sutration (>) 减法 (>) For any numers a and, a + = + a 对任意数 a 和,a + = + a For any numers a and, a = a. 对任意数 a 和,a = a. For any numers a,, and, (a + ) + = a + ( + ). 对任意数 a,, 和, (a + ) + = a + ( + ). For any numers a,, and, (a ) = a ( ). 对任意数 a,, 和, (a ) = a ( ). For any numers a,, and, a( + ) = a + a and a( ) = a a. 对任意数 a,, 和, a( + ) = a + a 且 a( ) = a a. For any numer a, there is exatly one numer a suh that a + ( a) = 0. 对任意数 a, 有且仅有一个数字 -a, 使得 a + ( a) = 0. For any numer a, where a, 0, there is exatly one numer a suh that a a =. 对任意数 a, 只要 a, 0, 则有且仅有一个数字 a, a 使得 a =. For any numer a, a 0 = 0 a = 0. 对任意数 a, a 0 = 0 a = 0. For any numers a,, and, if a =, then a + = +. 对任意数 a,, 和, 如果 a =, 则 a + = +. For any numers a,, and, if a =, then a =. 对任意数 a,, 和, 如果 a =, 则 a =. For any numers a,, and, with 0, if a =, then a = and a =. 对任意数 a,, 和, 0, 如果 a =, 则 a = 且 For any numers a,, and, if a >, then a + > +. 对任意数 a,, 和, 如果 a >, 则 a + > +. For any numers a,, and, if a >, then a >. 对任意数 a,, 和, 如果 a >, 则 a >. a =.

4 Perimeter and Cirumferene 周长和圆周 Area 面积 Lateral Surfae Area Division and Multipliation (>) 除法和乘法 (>) Zero Produt 零结果 Square 正方形 Retangle 长方形 irumferene of a irle 圆周长 Square 正方形 Retangle 长方形 Parallelogram 平行四边形 Trapezoid 梯形 Rhomus 菱形 Triangle 三角形 Regular polygon 正多边形 Cirle 圆形 Setor of a irle 扇形 Prism 棱柱体 For any numers a,, and,. if a > and > 0, then a > and a >.. if a > and < 0, then a < and a 对任意数 a,, 和, 如果 a > 且 > 0, 则 a > 且 a >. <. <. 如果 a > 且 < 0, 则 a < 且 a For any real numers a and, if a = 0, then a = 0, = 0, or oth a and equal zero. 对任意实数 a 和, 如果 a = 0, 则 a = 0, = 0, 或 a 和都等于零 P = 4s P = l + w C = πr or C = πd C = πr 或 C = πd A = s A = lw or A = h A = lw 或 A = h A = h A = h( + ) A = d d or A = h A = d d 或 A = h A = h A = Pa A = πr A = N 360 πr L = Ph

5 侧面积 Total Surfae Area 总面积 Volume 体积 Measurement Conversions 度量单位换算 Cylinder 圆柱体 Pyramid 锥体 Cone 圆锥体 Prism 棱柱体 Cylinder 圆柱体 Cue 立方体 Pyramid 锥体 Cone 圆锥体 Sphere 球体 Cue 立方体 Retangular prism 矩形棱柱体 Prism 棱柱体 Cylinder 圆柱体 Pyramid 锥体 Cone 圆锥体 Sphere 球体 Length 长度 L = πrh L = Pl L = πrl T = Ph + B T = πrh + πr T = 6s T = Pl + B T = πrl + πr T = 4 πr V = s 3 V = lwh V = Bh V = πr h V = 3 Bh V = 3 πr h V = 4 3 πr3 kilometer =,000 meters 公里 =,000 米 meter = 00 entimeters 米 = 00 厘米 entimeter = 0 millimeters 厘米 = 0 毫米 foot = inhes 英尺 = 英寸 yard = 3 feet or 36 inhes 码 = 3 英尺 or 36 英寸 mile =,760 yards or 5,80 feet 英里 =,760 码 or 5,80 英尺

6 Temperature 温度 Volume and Capaity 体积和容积 Weight and Mass 重量和质量 Time 时间 Metri to Customary 公制与惯制的换算 Fahrenheit to Celsius 华氏温度 Celsius to Fahrenheit 摄氏转换为华氏 liter =,000 milliliters 公升 =,000 毫升 kiloliter =,000 liters 千升 =,000 公升 kilogram =,000 grams 公斤 =,000 克 gram =,000 milligrams 克 =,000 毫克 metri ton =,000 kilograms 公吨 =,000 公斤 minute = 60 seonds 分钟 = 60 秒 hour = 60 minutes 小时 = 60 分 day = 4 hours 天 = 4 小时 meter inhes 米英寸 kilometer 0.6 mile 公里 0.6 英里 entimeter 0.39 inh 厘米 0.39 英寸 C = 95 (F 3) F = 59 C + 3 up = 8 fluid ounes 杯 = 8 液盎司 pint = ups 品脱 = 杯 quart = pints 夸脱 = 品脱 gallon = 4 quarts 加仑 = 4 夸脱 pound = 6 ounes 磅 = 6 盎司 ton =,000 pounds 吨 =,000 磅 week = 7 days 周 = 7 天 year = months or 5 weeks or 365 days 年 = 个月或 5 周或 365 天 leap year = 366 days 闰年 = 366 天 kilogram. pounds 千克. 磅 gram = oune 克 = 盎司 liter.057 quarts 公升.057 夸脱

A Acute angle 锐角 Acute triangle 锐角三角形 Algebraic expression 代数表达式 Algebraic modeling 代数模型 Alternate angles 内错角 Altitude 高 Angle bisector 角平分线 Angle of

A Acute angle 锐角 Acute triangle 锐角三角形 Algebraic expression 代数表达式 Algebraic modeling 代数模型 Alternate angles 内错角 Altitude 高 Angle bisector 角平分线 Angle of declination/depression 俯角 Angle of elevation/inclination