Elementary Trigonometry |
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Page 1
... figure is capable of revolving abc it the point 0 , and suppose that in this way it has passed successively from the posi- tion OA to the positions occupied by OB , OC , OD , .. then the angle between OA and any position such as OC is ...
... figure is capable of revolving abc it the point 0 , and suppose that in this way it has passed successively from the posi- tion OA to the positions occupied by OB , OC , OD , .. then the angle between OA and any position such as OC is ...
Page 7
... figure any ratio at sight . In the adjoining figure , PQR is a right - angled triangle in which PQ = 13 , PR = 5 , QR = 12 . Since PQ is the greatest side , R is the right angle . The trigonometrical ratios of the angles P and Q may be ...
... figure any ratio at sight . In the adjoining figure , PQR is a right - angled triangle in which PQ = 13 , PR = 5 , QR = 12 . Since PQ is the greatest side , R is the right angle . The trigonometrical ratios of the angles P and Q may be ...
Page 8
... figure we have a2 = b2 + c2 , so that if the lengths of two sides of a right - angled triangle are known , this equation will give the length of the third side . Example 1. ABC is a right - angled triangle of which C is the right angle ...
... figure we have a2 = b2 + c2 , so that if the lengths of two sides of a right - angled triangle are known , this equation will give the length of the third side . Example 1. ABC is a right - angled triangle of which C is the right angle ...
Page 13
... figure we have BC tan A : = ... tan A = a α с с AC b = sin A ÷ cos A ; = sin A cos A ' AC b b α Again , cot A = = BC α с с = cos A ÷ sin A cos A ... cot A = sin A ; ; = which is also evident from the reciprocal relation cot A = Example ...
... figure we have BC tan A : = ... tan A = a α с с AC b = sin A ÷ cos A ; = sin A cos A ' AC b b α Again , cot A = = BC α с с = cos A ÷ sin A cos A ... cot A = sin A ; ; = which is also evident from the reciprocal relation cot A = Example ...
Page 14
... , since the first factor is equal to 1 . - Example 2. Prove that cot a 1 - cos2 a = cos a . cot a 1 - cos2a = cot a × sin a COS a x sin a = cos a . 26. To prove that sec2 A With the figure of sin a 14 [ CHAP . ELEMENTARY TRIGONOMETRY .
... , since the first factor is equal to 1 . - Example 2. Prove that cot a 1 - cos2 a = cos a . cot a 1 - cos2a = cot a × sin a COS a x sin a = cos a . 26. To prove that sec2 A With the figure of sin a 14 [ CHAP . ELEMENTARY TRIGONOMETRY .
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Common terms and phrases
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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