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DOKUZ EYLUL UNIVERSITY SCHOOL OF MARITIME BUSINESS AND MANAGEMENT DEPARTMENT OF DECK E.Gürel Logarithmic and Trigonometric Functions

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E.Gürel Logarithmic Function 10 4 = 10, = 1, = = = = 0,1 = 1/ = 0,01 = 1/ = 0,001= 1/ = 0,0001= 1/ = 0,00001= 1/100000

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DOKUZ EYLUL UNIVERSITY SCHOOL OF MARITIME BUSINESS AND MANAGEMENT DEPARTMENT OF DECK E.Gürel Logarithmic Function Log 10 10,000 (10 4 )= 4 Log 10 1,000 (10 3 )= 3 Log (10 2 )= 2 Log (10 1 )= 1 Log 10 0,1 (10 -1 )= -1 Log 10 0,01 (10 -2 )= -2 Log 10 0,001 (10 -3 )= -3 Log 10 0,0001 (10 -4 )= -4 Log 10 1 = 0

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DOKUZ EYLUL UNIVERSITY SCHOOL OF MARITIME BUSINESS AND MANAGEMENT DEPARTMENT OF DECK E.Gürel The index of the log of any given number is one less than the number of figures before the decimal point in the given number. Log ,37= 3, Log ,054= 2, Log 10 73,0956= 1, Log 10 5,65473 = 0,

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DOKUZ EYLUL UNIVERSITY SCHOOL OF MARITIME BUSINESS AND MANAGEMENT DEPARTMENT OF DECK E.Gürel If the index of the log is less than 1. The number of figures is the how many number of zero the decimal point in the given number. Log 10 0,87635= - 1, Log 10 0,02536= - 2, Log 10 0,00234= - 3, Log 10 0,00053 = - 4,

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DOKUZ EYLUL UNIVERSITY SCHOOL OF MARITIME BUSINESS AND MANAGEMENT DEPARTMENT OF DECK E.Gürel The index of the log is obtained in the given number. Then find the matrix with using Nories Table. Log = 3,73062 Log ,8= 2,73062 Log 10 53,78= 1,73062 Log 10 5,378= 0,73062 Log 10 0,5378= - 1,73062 Log 10 0,05378= - 2,73062 Log 10 0,005378= - 3,73062 Log 10 0, = - 4,73062

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DOKUZ EYLUL UNIVERSITY SCHOOL OF MARITIME BUSINESS AND MANAGEMENT DEPARTMENT OF DECK E.Gürel

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E.Gürel

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E.Gürel Example 1: Log 5794,5 = ? Log 5794,5 = 3, , = 3, = 3,76302

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DOKUZ EYLUL UNIVERSITY SCHOOL OF MARITIME BUSINESS AND MANAGEMENT DEPARTMENT OF DECK E.Gürel Example 2: 3,73572= Log ? 3,73572 = 5441,5 Log 5541, = 4

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DOKUZ EYLUL UNIVERSITY SCHOOL OF MARITIME BUSINESS AND MANAGEMENT DEPARTMENT OF DECK E.Gürel The use of logs If a x b = c, then Log a + Log b = Log c 3 x 4 = 12, then Log 3 + Log 4 = Log 12 3 x 4 = 12 Log 3 + Log 4 = Log 12 Log 3 = 0,47712 Log 4 = 0,60206 Log 12= 1,07918

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DOKUZ EYLUL UNIVERSITY SCHOOL OF MARITIME BUSINESS AND MANAGEMENT DEPARTMENT OF DECK E.Gürel If a ÷ b = c, then Log a - Log b = Log c 12 ÷ 3 = 4, then Log 12 - Log 3 = Log 4 12 ÷ 3 = 4 Log 12 - Log 3 = Log 4 Log 12= 1,07918 Log 3 = 0,47712 Log 4 = 0,60206 The use of logs

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DOKUZ EYLUL UNIVERSITY SCHOOL OF MARITIME BUSINESS AND MANAGEMENT DEPARTMENT OF DECK E.Gürel Trigonometric Function Logarithmics values might also be pointed out here that the logs sin, cos, tan, etc., of < A may be derived from their natural number, and we would learn the student to the explanation on how to use these Tables. (Nories Table) Log sin ,7 = 8,45798 Log tan ,5 = 8,55205 Log cosec ,4 = 10,35702 Log sec ,3 = 10,04850 Log cot ,0 = 9,72354

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DOKUZ EYLUL UNIVERSITY SCHOOL OF MARITIME BUSINESS AND MANAGEMENT DEPARTMENT OF DECK E.Gürel

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E.Gürel

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E.Gürel

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E.Gürel

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E.Gürel Example 3: Log sin ,8= ? 9, = 9, ?

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DOKUZ EYLUL UNIVERSITY SCHOOL OF MARITIME BUSINESS AND MANAGEMENT DEPARTMENT OF DECK E.Gürel Example 4: 9,70521 = sin ? Sin , – = 17

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DOKUZ EYLUL UNIVERSITY SCHOOL OF MARITIME BUSINESS AND MANAGEMENT DEPARTMENT OF DECK E.Gürel THIS PRESANTATION WAS PREPARED BY EVREN GÜREL E MAIL : : Mobile Phone: Phone :

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