## Elements of Plane Trigonometry |

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Page 33

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**formula**, which are sometimes called the formulæ of verification , are very useful : - since cos2 A + sin2 A and 2 sin A cos A = = 1 , : - sin 24 . By adding and subtracting we have cos2 A + 2 sin A cos A + sin2 A and cos2 A 2 sin A cos ... Page 34

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**formula**for the sin 34 ; or by the 10th proposition of the 4th book of Euclid . cos 18 ° = √ ( 1 − sin2 18 ° ) - = √ / { 1 - ' ( √5 — 1 ) } } = √ / 16-5 + 2√5–1 sin 36 ° = == 2 sin 18 ° cos 18 ° - 2 ( √√5 − 1 ) √ ( 5 + √ / 5 ) ... Page 35

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**formula**, page 34 , we may find the sin 15o . sin 15 ° = 1 - 15 √ ( 1 + sin 30 ° ) — √ ( 1 — sin 30 ° ) } = { } { √√ / ( 1 + } ) = { √ // ( 1 − 1 ) } - 1 ( √ / 23 - 12 ) = - √3-1 2 2√2 This might have been found by putting sin ... Page 38

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**formula**let A 9 ° , then , 2 A 1 sin 9 ° } { √ ( 1 + sin 18 ° ) — √ ( 1 — sin 18 ° ) } = 2 ― = 18 ° , 5- - } { √ / ( 1 + √ 3 — 1 ) - √ // ( 1 — ~ 5 — 1 ) } 4 } { √ ( 3 + √ / 5 ) −√ ( 5 — √5 ) } ; = .. 4 sin 9 ° √ ( 3 + ... Page 45

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**formula**, page 29 , sin A + sin 5A = 2 sin 34 cos 24 , cos A + cos 5A = 2 cos 34 cos 2A , sin A + sin 34 + sin 54 = sin 34 + 2 sin 34 cos 24 , = sin 34 ( 1 + 2 cos 24 ) , cos A + cos 34 + cos 5A = cos 34 + 2 cos 34 cos 24 = cos 34 ( 1 + ...### Other editions - View all

### Common terms and phrases

1+tan AB² AC² angle ACB AP AP AP AP² ARITHMETIC Asin Atan B+cot centre circular measure circumference cos² cos³ cosec cosine cot 4+cot cot A cot cot² OCA diameter distance equal equation Euclid feet Find the number formula given GRAMMAR height Hence hexagon inscribed circle IVY LANE J. R. Young King's College School log blog logarithms nth root number of degrees number of sides perimeter perpendicular plane triangle quadrant radii radius ratio regular polygon Rudimentary Treatise sec² shew sin A cos sin A sin sin¹ sin2 sin² 18 sin³ sine and cosine square subtend subtracted T. H. L. Leary tan-¹ tan² tangent triangle ABC Trigonometry unity VIRTUE BROTHERS W. D. Hamilton

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