OF: HITMAN edit a geometric coordinate plane intersects the vertical axis, let an arbitrary point on the plane using a set of real numbers represented. The intersection of the axis is (0, 0), called the origin. The position in the horizontal and vertical direction, which is represented by x and y, respectively. A straight line can be represented by equation Y = Mx C, M is a slope of a straight line (gradient). This straight line exchanges (0, c) with the Y axis, intersecting (-C / m, 0) with the X-axis. The equation of the vertical line is x = k, x is the value. By (X0, Y0) this, the straight line of the slope is N-Y-Y0 = N (X-X0) a straight line is perpendicular to the slope of N, and its slope is -1 / n. The straight lines of (x1, y1) and (x2, y2) are y = (Y2-Y1 / X2-x1) (X-X2) Y2 x1 ≠ X2 If the slope of the two lines is M and N, then they The angle θ is satisfied with the Tan θ = M-N / 1 Mn radius of R, the center of the center in (a, b), indicated in (X-a) 2 (Y-B) 2 = R2. The coordinates in the three-dimensional space are similar to the two-dimensional space, which is just a z-axis, such as the ball having a radius of R, central position in (A, B, C), with (X-a) 2 (Y-B) 2 ( Z-C) 2 = R2. The three-dimensional space plane is generally AX BY CZ = D. The triangular side length is a right triangle of A, B, and C, one of which is θ. Its six triangle functions are: sine, cosine, cosecant, positive cut (SECANT), and Cotangent. SIN θ = B / c cos θ = a / c Tan θ = B / a CSCθ = C / B sec θ = C / a cotθ = A / B Range a radius of 1, the sinusoidal and cosine are high and bottom of the right angle triangle, respectively. . A = cos θ b = sin θ In accordance with the pycloth theorem, we know A2 B2 = C2.
Therefore, for any angle θ on the circle, we can obtain the following equation: COS2θ SIN2θ = 1 Triangle constant equation According to the definition described in the previous few pages, it can obtain the following constant equation (Identity): Tan θ = sin θ / cos θ, cotθ = COS θ / SIN θ SEC θ = 1 / cos θ, CSCθ = 1 / sin θ separates COS 2θ SiN 2θ = 1 with CoS 2θ and SiN 2θ, can be obtained: SEC 2θ-TAN 2θ = 1 and CSC 2θ-Cot 2θ = 1 for negative angles The six triangles functions are: sin (-θ) = -SIN θ CSC (-θ) = -CSCθ COS (-θ) = COS θ SEC (-θ) = sec θ TAN (-θ) = -tan θ COT (-θ ) = -Cot θ When two angles are added, the use and angular formula: sin (α β) = sinαcosβ COSαSINβ COS (α β) = COSαCOSβ-SinαSinβ TAN (α β) = Tanα Tanβ / 1-TanαTanβ If you encounter two times or triple angle, Magic formula: sin2α = 2SINαCOSα SIN3α = 3SINα COS2α-Sin3α COS2α = CoS 2α-SiN 2α COS3α = CoS 3α-3Sin 2αcoosα TAN 2α = 2tanα / 1-TAN 2α TAN3α = 3TANα-TAN 3α / 1-3TAN 2α 2D pattern below Some two-dimensional graphics perimeters and area formulas. Circle: radius = r diameter D = 2R circumference = 2πr = πD area = πR2 (π = 3.1415926 ......) Elliptical: Area = πAB A and B represent half of the short axis and the long axis, respectively. Rectangle: Area = AB permele = 2A 2B Parallelogram: Area = BH = ab Sinα Perpetance = 2A 2B Trapezoid: Area = 1 / 2H (A B) Perimeter = A B H (SECα SECβ) Positive N Side: Area = 1 / 2NB2 COT (180 ° / N) perimeter = NB quadrilateral (I): area = 1/2Ab sinα quadrilateral (II): Area = 1/2 (H1 H2) B AH1 CH2 3D graphics The following is a three-dimensional stereo volume and surface area (including The bottom) formula.
