Trigonometry |
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Page 11
... circle of radius 5. ] 2. Is there an acute angle whose sine is any given positive number ? Prove that your answer is correct . 3. Construct angles whose tangents are ( a ) 3/10 ; ( b ) 1/2 ; ( c ) 2/3 ; ( d ) 1 ; ( e ) 10/3 ; ( ƒ ) 2 ...
... circle of radius 5. ] 2. Is there an acute angle whose sine is any given positive number ? Prove that your answer is correct . 3. Construct angles whose tangents are ( a ) 3/10 ; ( b ) 1/2 ; ( c ) 2/3 ; ( d ) 1 ; ( e ) 10/3 ; ( ƒ ) 2 ...
Page 12
... circle , radius = 10 , center at 0 . Draw AT perpendicular to Ox and tangent to this circle . Given * It is often said that the tangent of 90 ° , for example , is infinite ; this ex- pression does not give any value to the tangent at 90 ...
... circle , radius = 10 , center at 0 . Draw AT perpendicular to Ox and tangent to this circle . Given * It is often said that the tangent of 90 ° , for example , is infinite ; this ex- pression does not give any value to the tangent at 90 ...
Page 13
... circle and the tan- gent AT , P and Q , respectively ; then the ordinate ( y ) of the point P can be read to tenths , and this divided by r = 10 gives the value of sin a to two decimal places . Similarly , the abscissa ( x ) of P can be ...
... circle and the tan- gent AT , P and Q , respectively ; then the ordinate ( y ) of the point P can be read to tenths , and this divided by r = 10 gives the value of sin a to two decimal places . Similarly , the abscissa ( x ) of P can be ...
Page 14
... circle Check . 5. The radius of a circle is 7 ft . 11 ft . long subtend at the center ? 6. From the top of a cliff 92 ft . in height the angle of depression of a boat at sea is observed to be 20 ° . How far out is the boat ? Check . 7 ...
... circle Check . 5. The radius of a circle is 7 ft . 11 ft . long subtend at the center ? 6. From the top of a cliff 92 ft . in height the angle of depression of a boat at sea is observed to be 20 ° . How far out is the boat ? Check . 7 ...
Page 20
... circle is 21.5 ft . , the angle which it subtends at the center is 41 ° . Find the radius of the circle . 4. To determine the width BA of a river , a line BC 100 rods long is laid off at right angles to a line from B to some object A on ...
... circle is 21.5 ft . , the angle which it subtends at the center is 41 ° . Find the radius of the circle . 4. To determine the width BA of a river , a line BC 100 rods long is laid off at right angles to a line from B to some object A on ...
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Common terms and phrases
acute angle angle of elevation angle opposite angular speed Arccos Arcsin Arctan called circle colog cologarithm components congruent angles construct coördinates cos² cotangent Denote determine equal equation Example EXERCISES Find the angle Find the distance following triangles formulas geometry given angle given side graph hence hypotenuse included angle initial point initial side law of cosines law of sines law of tangents length magnitude mantissa method negative numerical measure obtuse angle perpendicular plane polar triangle positive angle Proj Prove Quad radian measure radius resultant revolutions revolutions per minute right angle right triangle rotation sec² second quadrant segment side opposite simple harmonic motions sin² solution spherical triangle subtends subtract tabular difference terminal side theorem tion trigonometric functions vertex vertical whence x-axis y-axis zero
Popular passages
Page 137 - The logarithm of a product is equal to the sum of the logarithms of its factors.
Page 137 - The characteristic of a number less than 1 is found by subtracting from 9 the number of ciphers between the decimal point and the first significant digit, and writing — 10 after the result. Thus, the characteristic of log...
Page 32 - In any triangle the square of any side is equal to the sum of the squares of the other two sides minus twice the product of these two sides and the cosine of their included angle.
Page 113 - Spherical Triangle the cosine of any side is equal to the product of the cosines of the other two sides, plus the product of the sines of those sides into the cosine of their included angle ; that is, (1) cos a = cos b...
Page 2 - LOGARITHMS ing the proportional part corresponding to the fourth figure to the tabular number corresponding to the first three figures. There may be an error of 1 in the last place. N 0 1 2 3 4 5 6 7 8 9 123 456 789 55...
Page 87 - 1 — cos a 1 + cos a 1 + cos a * 1 + cos a sin a 16. If a numerical value of any function of a is given, all the other functions of a and of a/2 can be found geometrically from Ex. 14. Thus, if sin a = 4/5 is given, lay off OP = 5, BP = 4 ; then 07? = V52 — 4* = 3. Hence, 073 = 8, AB=2; and CP = v
Page xvii - ... duplicates of the preceding fiveplace tables, reduced to four places, and with larger intervals between the tabulations. The value of such four-place tables consists in the greater speed with which they can be used, in case the degree of accuracy they afford is sufficient for the purpose in hand.
Page 42 - The area of a triangle is equal to one half the product of the base and the altitude: A = I bx a.
Page 137 - The logarithm of the root of a number is found by dividing the logarithm of the number by the index of the root. For, \ Therefore, tag tfï = 2 = 6.
Page 137 - In brief : to multiply, add logarithms. II. The logarithm of a fraction is equal to the difference obtained by subtracting the logarithm of the denominator from the logarithm of the numerator : log (a/6) = log a — log 6.