Plane and Spherical Trigonometry

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McGraw-Hill, 1916 - 188 páginas
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Contenido

Signs of the trigonometric functions
15
Trigonometric functions by computation
16
Given the function of an angle to construct the angle
20
Trigonometric functions applied to right triangles
22
Relations between the functions of complementary angles
23
Given the function of an angle in any quadrant to construct the angle
24
Fundamental relations between the functions of an angle
27
To express one funotion in terms of each of the other functions
29
Transformation of trigonometric expressions so as to contain but one function
31
Identities
32
Inverse trigonometric functions
34
Vectors
53
CHAPTER IV
61
Proof of the reduction formulas for any value of 0
68
Changes in the value of the sine and cosine as the angle increases
74
CHAPTER V
83
Derivation of the formulas for sine and cosine of the difference of two angles
84
Proof of the addition formulas for other values of the angles
85
Proof of the subtraction formulas for other values of the angles
86
Formulas for the tangents of the sum and the difference of two angles
89
Functions of an angle in terms of functions of half the angle
90
Functions of an angle in terms of functions of twice the angle
92
Sum and difference of two like trigonometric functions as a product
94
To change the product of functions of angles to a sum
97
Relation between sin 0 0 and tan 0
100
CHAPTER VI
101
Cosine theorem
103
Case II The solution of a triangle when two sides and an angle opposite one of them are given
105
Case III The solution of a triangle when two sides and the included angle are given First method
109
Case III Second method
110
Case III Third method
112
Case IV The solution of a triangle when the three sides are given
113

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Página 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.
Página 139 - The cube root of a number is one of the three equal factors of the number. Thus the cube...
Página 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.
Página 101 - Law of Sines — In any triangle, the sides are proportional to the sines of the opposite angles. That is, sin A = sin B...
Página 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...
Página 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.
Página 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.
Página 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.
Página 161 - Spherical Triangle the cosine of any side is equal to the product of the cosines of the other two sides...
Página 14 - The logarithm of the reciprocal of a number is called the Cologarithm of the number.

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