By Ben zion Kon
"By indirections locate path out"-(Shakespeare, Hamlet, Act 2, Scene 1) This guide is a reference paintings during which the reader can locate definitions and genuine info in numerous fields of arithmetic. the aim of this ebook is twofold: it really is designed for fast connection with mathematical recommendations: definitions, principles, formulation and theorems with examples. it could function a guide for college kids for sensible functions (homework, tests, etc).
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Cotangent is an odd periodic function with a period (Figure 12). Figure 11 Figure 12 e. Increase and Decrease Domains and Denotations of Trigonometric Functions Quarter f. Basic Formulas 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. g. Reduction Formulas h. Additional Formulas 1. , where is satisfy the equations , and 2. 3. 4. 5. i. Expressing Trigonometric Function Through Another Computed through In these formulas, the root's mark is the same as that of the left side of the function, which depends on the quarter being .
3. If , then the equation obtained is a. If , then it forms two parallel straight lines. b. If , then it forms two coincident lines. c. If , then the equation holds for no point. 1 Vector Concept a. A vector is a defined quantity with both direction and magnitude. b. It is graphically represented by a directional segment, that is, a segment with an arrow on one end, representing the direction of the vector. c. The absolute value of a vector is called the length or a vector. d. Vectors are denoted by small, bold Latin characters , and modules are denoted as .
D. 7 Inner (Scalar) Product a. The inner product of two vectors , is scalar ( dot ), defined as: when is the angle between the vectors. b. , when is the projection of on , and is the projection of on . c. Vectors and are mutually perpendicular if, and only if, . d. If and , then: . e. , ( is a scalar). f. g. 8 Cross (Vector) Product a. Cross product of vectors , is vector denoted as ( cross ), which holds: 1. , when is the angle between vectors , . In other words, the length of vector equals the area of the parallelogram with vectors for sides.
University Mathematics Handbook by Ben zion Kon