## Plane Trigonometry |

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acute angle altitude angle of depression angle of elevation antilog apothem chord circle colog cologarithm computed cos x cos¹ cos² cosecant cosine cot² cotangent Cotg csc² decimal diagonal examples Exercise figure Find antilog Find log find the angle Find the area Find the distance Find the height Find the numerical Find the side Find the value five-place tables formula four-place tables geometry given angle given number Hence history of trigonometry horizontal plane hypotenuse isosceles triangle law of sines Let the pupil log cot loga logarithms mantissa method minutes negative numerical value oblique triangles obtained parallelogram Prove radians radius Regiomontanus right triangle sec² secant Similarly sin-¹ sin² sin³ sine solution subtends Subtract tan x tan² Tang tangent tower triangle ABC trigonometric functions

### Popular passages

Page 10 - If the number is less than 1, make the characteristic of the logarithm negative, and one unit more than the number of zeros between the decimal point and the first significant figure of the given number.

Page 167 - The circumference of a circle is supposed to be divided into 360 equal parts, called degrees; each degree into 60 minutes, and each minute into 60 seconds. Degrees, minutes, and seconds are designated by the characters °, ', ". Thus 23° 14' 35" is read 23 degrees, 14 minutes, and 35 seconds.

Page 89 - ... cos x. In applying the above general rule to any particular example it will be found that the algebraic sign of the result is the same as the sign of the original function. Thus, sin 330° = sin (360° - 30°) = - sin 30°, the short way of determining the sign of sin 30° being to note that sin 330° is -negative since 330° is in the fourth quadrant and that sin 30° must have the same sign as sin 330°. If geometrical proofs for the above reduction formulas are, desired, such proofs may be...

Page 14 - 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 111 - Sines that the bisector of an angle of a triangle divides the opposite side into parts proportional to the adjacent sides.

Page 21 - What is the side of a square whose area is equal to that of a circle 452 feet in diameter ? Ans. ^(452)

Page 108 - In the same way it may be proved that a : b : : sin. A : sin. B, and these two proportions may be written a : 6 : c : : sin. A : sin. B : sin. C. THEOREM III. t8. In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference. By Theorem II. we have a : b : : sin. A : sin. B.

Page 122 - If R is due east from P, what is the direction of each place from every other place? If R is NE from P, what would each of these directions be ? 21. What angle is subtended by an island 2 miles long as viewed from a point 3 miles distant from one end of the island and 4 miles from the other end ? 22. Make up two practical problems which can be solved by the method of Case III and solve them, CASE IV. GIVEN Two SIDES AND AN ANGLE OPPOSITE ONE OF THEM 82. The Solution of Case IV, like that of Case...

Page 70 - ... 12. A ladder 32 ft. long is leaning against a house, and reaches to a point 24 ft. from the ground. Find the angle between the ladder and the wall. 13. A man whose eye is 5 ft. 8 in. from the ground is on a level with, and 120 ft. distant from, the foot of a flag pole 45 ft. 8 in. high. What angle does the direction of his gaze, when he is looking at the top of the pole, make with a horizontal line from his eye to the pole ? 14. Find the...

Page 10 - Hence, the characteristic of an integral or mixed number is one less than the number of figures to the left of the decimal point. 5. Characteristic of a Decimal Fraction. 1 = 10°.