Elementary TrigonometryMacmillan and Company, 1893 - 404 páginas |
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Página xiv
... increases from 0 to 267 0 π Distance and Dip of the Visible Horizon 269 Chapter XXII . GEOMETRICAL PROOFS . Expansion of tan ( A + B ) • 273 • Formulæ for transformation of sums into products 274 PAGE Proofs by Projection • Proof of the ...
... increases from 0 to 267 0 π Distance and Dip of the Visible Horizon 269 Chapter XXII . GEOMETRICAL PROOFS . Expansion of tan ( A + B ) • 273 • Formulæ for transformation of sums into products 274 PAGE Proofs by Projection • Proof of the ...
Página 73
... XC Again , if x is a quantity which gradually increases and finally becomes infinitely large , the fraction becomes infinitely small ; α X that is , α when x = ∞ , the limit of = 0 . X 83. DEFINITION . If y is a function of x.
... XC Again , if x is a quantity which gradually increases and finally becomes infinitely large , the fraction becomes infinitely small ; α X that is , α when x = ∞ , the limit of = 0 . X 83. DEFINITION . If y is a function of x.
Página 75
... increase and OM decrease . When OP comes into coincidence with OF the angle POM becomes equal to 90 ° , and OM vanishes , while MP becomes equal to OP . Hence And OP sin 90 ° = = OP 1 ; cos 90 ° : tan 90 ° cot 90 ° sec 90 ° cosec 90 ...
... increase and OM decrease . When OP comes into coincidence with OF the angle POM becomes equal to 90 ° , and OM vanishes , while MP becomes equal to OP . Hence And OP sin 90 ° = = OP 1 ; cos 90 ° : tan 90 ° cot 90 ° sec 90 ° cosec 90 ...
Página 76
... increases from 0 ° to 360 ° . Let XX and YY ' be two straight lines intersecting at right angles in O. X M M M M X With centre O and any radius OP describe a circle , and suppose the angle A to be traced out by the revolution of OP ...
... increases from 0 ° to 360 ° . Let XX and YY ' be two straight lines intersecting at right angles in O. X M M M M X With centre O and any radius OP describe a circle , and suppose the angle A to be traced out by the revolution of OP ...
Página 77
... increases from 0 ° to 360 ° . changes . cos.180 = -1 cos 90 ° = 0 cos A negative cos A positive and increasing and decreasing cos A negative cos A positive and decreasing and increasing cos 270 = 0 cos 0 = 1 89. To trace the changes in ...
... increases from 0 ° to 360 ° . changes . cos.180 = -1 cos 90 ° = 0 cos A negative cos A positive and increasing and decreasing cos A negative cos A positive and decreasing and increasing cos 270 = 0 cos 0 = 1 89. To trace the changes in ...
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1+cos 1+tan² a+cos A+tan acute angle angle of elevation B+cos centre circle College cos² cos³ cosec cosine cot² cyclic quadrilateral decimal denote diff equal equation ex-central triangle Example expression Fcap feet Find the angle find the distance find the height Find the number Find the value flagstaff following identities formula given log greatest angle Hence horizontal plane hypotenuse inscribed LAOB loga logarithm magnitude miles negative number of radians observer pedal triangle perpendicular polygon positive Prof Prove the following quadrant quadrilateral radian measure radius vector regular polygon right angle right-angled triangle sec² sexagesimal shew sides sin sin sin sin² sin³ sine solution solve the triangle subtends an angle supplementary angles tan² tangent tower triangle ABC trigono trigonometrical functions trigonometrical ratios π π
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