## Plane and Spherical Trigonometry |

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ABC Fig absolute value acute angle altitude angle of depression angle of elevation azimuth centre colog computed cos x cos² cosecant cosine cotangent cotx csc b csc denote earth's ecliptic equal equation equinoctial example EXERCISE feet find the angles Find the area Find the distance Find the height Find the value formulas Given Hence horizontal plane hour angle hypotenuse included angle inscribed isin Law of Sines Leaving latitude length logarithms loge longitude meridian miles moving radius Napier's Rules negative observer obtain opposite perpendicular pole Prove radians regular polygon right ascension right spherical triangle right triangle secant ship sails sin A sin sin² solution solve the triangle sphere star subtended tan² tanc tangent tower trigonometric functions TRIGONOMETRY unit circle vertical whence x+tan

### Popular passages

Page 149 - Substituting these values of cosp cos m and cosp sin m in the value of cos a, we obtain cos a = cos b cos с + sin b sin с cos A ') and similarly, cos b = cos a cos с -f- sin a sin с cos В > [45] cos с = cos a cos b -\- sin a sin b cos С J 3.

Page 61 - Sines that the bisector of an angle of a triangle divides the opposite side into parts proportional to the adjacent sides.

Page 148 - That is. the sines of the sides of a spherical triangle are proportional to the sines of the opposite angles.

Page 139 - I. The sine of the middle part is equal to the product of the tangents of the adjacent parts.

Page 52 - Formulas [4]-[ll] may be combined as follows : sin (x ± y) = sin x cos y ± cos x sin y, cos (x...

Page 26 - The area of a triangle is equal to one-half the product of the base by the altitude ; therefore, if a and b denote the legs of a right triangle, and F the area, F = \ ab.

Page 60 - The square of any side of a triangle is equal to the sum of the squares of the other two sides, diminished by twice the product of the sides and the cosine of the included angle.

Page 50 - ... y cos x cos y — sin x sin y tan a- + tan y 1 — tan x tan y sin (x — y) = sin x cos y — cos x...

Page 174 - For (Fig. 50) the angle ZOB between the zenith of the observer and the celestial equator is obviously equal to his latitude, and the angle POZ is the complement of ZOB. The arc NP being the complement of PZ, it follows that the altitude of the elevated pole is equal to the latitude of the place of observation. The triangle ZPM then (however much it may vary in shape for different positions of the star M ) always contains the following five magnitudes : PZ= co-latitude of observer = 90°...

Page 116 - 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)