Plane and Spherical Trigonometry |
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Page 2
... lines X'X and Y'Y . These parts are called first , second , third , and fourth quadrants , respectively . They are placed as shown by the Roman numerals in Fig . 2 . If OX is taken as the initial side of an 2 PLANE TRIGONOMETRY.
... lines X'X and Y'Y . These parts are called first , second , third , and fourth quadrants , respectively . They are placed as shown by the Roman numerals in Fig . 2 . If OX is taken as the initial side of an 2 PLANE TRIGONOMETRY.
Page 11
... fourth quadrant , the abscissa is positive and the ordinate is negative . This is shown in the following table : Quadrant Abscissa Ordinate Y ++ II III +1 IV +1 Y ' FIG . 11 . r x M P 2 -X Thus , in Fig . 10 , P1 , P2 , P3 , and P4 are ...
... fourth quadrant , the abscissa is positive and the ordinate is negative . This is shown in the following table : Quadrant Abscissa Ordinate Y ++ II III +1 IV +1 Y ' FIG . 11 . r x M P 2 -X Thus , in Fig . 10 , P1 , P2 , P3 , and P4 are ...
Page 15
... fourth quadrant . In a similar manner the algebraic signs of the remaining func- tions of are determined . The student should verify the follow- ing table : Quadrant sin @ cos @ tan @ cot 0 sec @ csc @ I. II III IV + + 1 + 1 +11+ ++ 11 ...
... fourth quadrant . In a similar manner the algebraic signs of the remaining func- tions of are determined . The student should verify the follow- ing table : Quadrant sin @ cos @ tan @ cot 0 sec @ csc @ I. II III IV + + 1 + 1 +11+ ++ 11 ...
Page 26
... fourth quadrant . - sin cos 0 , when tan 0 = 2 and 0 is in csc2 0 , when cos 0 = and 0 is in = sec2 0 - sin @ 10. cot 0 + = csc 0 , when sin = √3 and is in the second 1 + cos 0 quadrant . 11. Find the value of sin @tan @ cos 0 cot 0 ...
... fourth quadrant . - sin cos 0 , when tan 0 = 2 and 0 is in csc2 0 , when cos 0 = and 0 is in = sec2 0 - sin @ 10. cot 0 + = csc 0 , when sin = √3 and is in the second 1 + cos 0 quadrant . 11. Find the value of sin @tan @ cos 0 cot 0 ...
Page 28
... fourth quadrant . √2 , and 0 in the first quadrant . — } , and 0 in the third quadrant . - 3 , and in the fourth quadrant . , and in the third quadrant . — , and a in the second quadrant . - , and ẞ in the fourth quadrant . — , and ...
... fourth quadrant . √2 , and 0 in the first quadrant . — } , and 0 in the third quadrant . - 3 , and in the fourth quadrant . , and in the third quadrant . — , and a in the second quadrant . - , and ẞ in the fourth quadrant . — , and ...
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Common terms and phrases
9 Prop abscissa acute angle amplitude cd log cot cd log tan circle co-a co-c co-ẞ colog cologarithm complex number Computation Construct coördinates cos¹ cos² cosh cosine cot cd log cotangent decimal distance Draw equal equation Example EXERCISES Express Find the value formulas Given horizontal hyperbolic functions hypotenuse imaginary unit initial side intersection log cot cd log cot log log tan cd log tan log logarithms M₁P₁ Mant mantissa measured miles modulus multiples Napier's rules negative nth root opposite ordinate P₁ plane polar triangle positive Prove radians radius right angle right spherical triangle right triangle sec² segment sin a sin sin ẞ sin² sin³ sine sinh Solution Solve sphere SPHERICAL TRIGONOMETRY Subtracting tabular difference tan-¹ tan² tangent terminal side trigonometric functions vector απ
Popular passages
Page 2 - Every circumference of a. circle, whether the circle be large or small, is supposed to be divided into 360 equal parts called degrees. Each degree is divided into 60 equal parts called minutes, and each minute into 60 equal parts called seconds.
Page 139 - The cube root of a number is one of the three equal factors of the number. Thus the cube...
Page 13 - To Divide One Number by Another, Subtract the logarithm of the divisor from the logarithm of the dividend, and obtain the antilogarithm of the difference.
Page 101 - Law of Sines — In any triangle, the sides are proportional to the sines of the opposite angles. That is, sin A = sin B...
Page 6 - When the number is greater than 1, the characteristic is positive, and is one less than the number of digits to the left of the decimal point...
Page 15 - To find any power of a given number, multiply the logarithm of the number by the exponent of the power. The product is the logarithm of the power.
Page 110 - In every plane triangle, the sum of two sides is to their difference as the tangent of half the sum of the angles opposite those sides is to the tangent of half their difference.
Page 4 - In it the right angle is divided into 100 equal parts called grades, the grade into 100 equal parts called minutes, and the minute into 100 equal parts called seconds.
Page 161 - Spherical Triangle the cosine of any side is equal to the product of the cosines of the other two sides...
Page 14 - The logarithm of the reciprocal of a number is called the Cologarithm of the number.