## Plane Trigonometry |

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### Common terms and phrases

angle corresponding angle whose logarithmic b₁ bottom c. d. log cot column marked log cosecant Cosine Sine Cosine cot c. d. log Cotang Tang Cotang degrees and minutes EXAMPLE 3.-Find EXAMPLES FOR PRACTICE f₁ feet Find the angle Find the logarithmic formula given function given logarithm horizontally opposite hypotenuse i(f₁ log cot c. d. log cot log log tan c. d. log tan log logarithmic cosine logarithmic cotangent logarithmic functions logarithmic sine logarithmic tangent natural functions number of degrees number of minutes number of odd number of seconds odd seconds ordinates p. p. log perpendicular ratio right triangle secant side adjacent side opposite Sine Cosine Sine SOLUTION SOLUTION.-The square subtracted table of logarithmic table of Natural tabular difference Tang Cotang Tang Tangents and Cotangents total number trapezoid trigono trigonometric functions vertex whence wwww wwwwwwwwww x₁ ΙΟ

### Popular passages

Page 5 - The sum of any two sides of a triangle is to their difference, as the tangent of half the sum of the angles opposite to those sides, to the tangent of half their difference.

Page 19 - ... towards the end of the table which increase by 10 units at a time, all interpolation is avoided, as with a glance at the table we can at once take out the required S or T. TABLE III. This table contains for every ten seconds of the quadrant the logarithms of the sines, cosines, tangents, and cotangents.

Page 5 - In any triangle, the square of the side opposite an acute angle is equal to the sum of the squares of the other two sides, minus twice the product of one of these sides and the projection of the other side upon it.

Page 3 - Law of Sines — In any triangle, the sides are proportional to the sines of the opposite angles. That is, sin A = sin B...

Page 20 - Hence, the area of a triangle is equal to one-half the product of any two sides ' and the sine of their contained angle. EXAMPLES. 1. Find the area of the triangle in which two sides are 31 ft. and 23 ft. and their contained angle 67° 30'.

Page 29 - K. The area of each trapezoid is equal to one-half the sum of its bases multiplied by its altitude, and the sum of their areas together with the area of the triangle is equivalent to the area of the polygon ABCDE F. In Fig. 318 a base line HP\s, drawn, and from each angle of the polygon perpendiculars are drawn to it.

Page 32 - Simpson's one-third rule," which is as follows : " Divide the base line into an even number of equal parts and erect ordinates at the points of division ; then add together the first and last ordinates, twice the sum of all the other odd ordinates, and four times the sum of all the even ordinates; multiply the sum by one-third of the common distance between ordinates.

Page 22 - For an angle between 45° and 90°, find the degrees at the bottom of the page and the minutes in the column (marked ') at the right of the page.

Page 57 - These formulas serve as the definitions of the trigonometric functions of any angle; that is, the sine of any angle is the ratio of the side opposite to the hypotenuse; the tangent is the ratio of the side opposite to the side adjacent, etc.