RIGHT TRIANGLE TRIGONOMETRY The word Trigonometry can be broken into the parts Tri‚ gon‚ and metry‚ which means “Three angle measurement‚” or equivalently “Triangle measurement.” Throughout this unit‚ we will learn new ways of finding missing sides and angles of triangles which we would be unable to find using the Pythagorean Theorem alone. The basic trigonometric theorems and definitions will be found in this portion of the text‚ along with a few examples‚ but the reader will frequently
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Spherical trigonometry Spherical trigonometry is that branch of spherical geometry which deals with the relationships between trigonometric functions of the sides and angles of the spherical polygons (especially spherical triangles) defined by a number of intersecting great circles on the sphere. Spherical trigonometry is of great importance for calculations in astronomy‚ geodesy and navigation. The origins of spherical trigonometry in Greek mathematics and the major developments in Islamic mathematics
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Symmetric: a = b → b = a or ∠A ∠B → ∠B ∠A Transitive: a = b and b = c → a = c or ∠A ∠B and ∠B ∠C → ∠A ∠C Definitions: Definition of Right Angles: ∠1 is a right angle ↔ m∠1 = 90° Definition of Perpendicular: ⟘ ↔ ∠1 is a right angle Definition of Congruent Segments: AB = BC ↔ Definition of Congruent Angles: m∠A m∠B ↔ ∠A ∠B Definition of Midpoint: X is the midpoint of ↔ AX = XB (or ) Definition of Supplementary: ∠1 and ∠2 are supplementary ↔ m∠1 +
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QUADRILATERAL: (□ABCD) Points A‚ B‚ C‚ D are called the vertices of □ABCD AB‚ BC‚ CD and AD are called the sides of ABCD AC‚ BD are called Diagonals of ABCD A‚ B‚C and D are the four angles of ABCD A Quadrilateral has 10 parts – 4 line segments‚ 4 angles‚ 2 diagonals. Sides of Quadrilateral are the subset of Quadrilateral. Angels of Quadrilateral are not a subset of a Quadrilateral. Diagonals of a Quadrilateral are not a subset of Quadrilateral. ADJACENT SIDES:
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resistance‚Good mach inability are used. High carbon steels‚ Steels coated with wear resisting metals like chromium‚ tungsten carbide Form measurements: straightness‚ flatness‚ squreness‚ circularity & cylindricity – Measurement of angles & tapers: sine bars‚ angle gauges: auto collimator‚ clinometer & spirit level; taper gauges‚ bevel protractors. FORM MEASUREMENTS Straightness Testing Straightedge A straightedge is a tool with an accurately straight edge used for drawing or cutting straight
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airborne. Projectile is the moving body in this kind of motion. It refers to any object thrown‚ launched or otherwise projected so that once released‚ if air resistance is neglected‚ its path is affected only by the Earth’s gravity. As fired at an angle‚ it is influenced by its horizontal inertia and vertical gravity. The projectile creates a parabolic curve. The curved path is known as the trajectory. We are assuming here that there is no or very little air resistance. The equations of motion for
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Math Exam Notes Unit 1 The Method of Substitution -Solving a linear system by substituting for one variable from one equation into the other equation -To solve a linear system by substitution: Step 1: Solve one of the equations for one variable in terms of the other variable Step 2: Substitute the expression from step 1 into the other equation and solve for the remaining variable Step 3: Substitute back into one of the original equations to find the value of the other variable Step
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one right angle If the sides are known instead of the angles‚ then L’Huiller’s Formula can be used to solve for the spherical excess 1 s s − a s − b s−c tan E = tan tan tan tan 2 2 2 2 2 a+b+c Where: s= 2 Solutions to Right Spherical Triangles (C = 90o) Sides a‚ b‚ c are based on the corresponding arc lengths S = rθ that is based on its corresponding interior angles S a = rθ BOC ; Sb = rθ AOC ; Sc = rθ AOB and that a + b + c < 360o Angles A‚ B‚ C of
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Lab Report Experiment Aim: To determine the acceleration of an object down an incline plane using various methods. Research Question: Is there a relationship between the angle θ of the incline and the acceleration down the plane? Equipment: * Ticker Timer (AC 50Hz ) * Incline (wood) * Meter ruler * Dynamic Trolley ( Mass: 380.55 ± 0.01g ) * Carbonated paper * Power Source (2W) * Data Logger * Motion Sensor * Tennis Ball Method
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Figures‚ Definitions‚ and Illustrations (Project in Math) Submitted by: Submitted to: Jericah Manalang Mrs. Joycelene Migano Table of Contents A. Introduction B. The Art of Reasoning C. The Models of Points‚ Lines‚ and Angles D. The Transversals E. Polygons 1. Triangle 2. Quadrilateral 3. Pentagon 4. Hexagon 5. Heptagon 6. Octagon 7. Nonagon 8. Decagon 9. Dodecagon 10. Tetradecagon F. Circles Introduction "Geometry
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