## Plane Trigonometry and Tables |

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### Common terms and phrases

9 log abscissa absolute value acute angle adjacent leg angle of depression angle of elevation circumference colog cologarithm column complementary angles Compute cos log cot cos(x cos² cos²x cosecant cot tan cot cotangent cotx departure equal equation EXAMPLE EXERCISE feet Find log Find the angle Find the area Find the distance Find the height Find the value formulas Hence horizontal hypotenuse included angle isosceles Law of Sines Leaving latitude log cos 9 log cot log log tan log loga logarithm loge longitude mantissa miles negative places of decimals plane radians radius regular polygon required number right triangle secant Sect SECTION ship sails sides significant figures sin² sin²x sine and cosine solution Solve subtended subtracting tan x tan-¹x tan² tangent tower TRIGONOMETRIC FUNCTIONS unit circle yards

### Popular passages

Page vi - 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 66 - The square of any side of a triangle is equal to the sum of the squares of the other two sides diminished by twice their product into the cosine of the included angle.

Page 67 - The bisector of an angle of a triangle divides the opposite side into segments proportional to the adjacent sides.

Page 65 - The sides of a triangle are proportional to the sines of the opposite angles.

Page 92 - A pole is fixed on the top of a mound, and the angles of elevation of the top and the bottom of the pole are 60° and 30° respectively. Prove that the length of the pole is twice the height of the mound.

Page 120 - X a" = am+". .'. log. (MX N) = m + n — log. M + log. N. Similarly for the product of three or more factors. (5) The logarithm of the quotient of two positive numbers is found by subtracting the logarithm of the divisor from the logarithm of the dividend. (6) The logarithm of a power of a positive number is found by multiplying the logarithm of the number by the exponent of the power. For, N" = (oT)

Page 120 - For, 2Р = (а")' = а"г. . • . loga (N") = np=plog„N. 7. The logarithm of the real positive value of a root of a positive number is found by dividing the logarithm of the number by the index of the root.

Page 31 - From the top of a hill the angles of depression of two successive milestones, on a straight level road leading to the hill, are observed to be 5° and 15°.

Page x - The difference between the two adjacent mantissas is 7, and the difference between the corresponding numbers is 1. The difference between the smaller mantissa, 82321, and the given mantissa, 82326, is 5. Therefore, the number to be annexed to 6656 is f of 1 = 0.7, and the fifth significant figure of the required number is 7.