Plane Trigonometry |
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abscissa absolute value acute angle adjacent leg angle in Quadrant angle of depression angle of elevation angles less circumscribed circle colog complementary angle Compute cos(x cos² cos²x cosecant cotangent cotx equal equation EXAMPLE EXERCISE find the angles Find the area Find the distance Find the functions Find the height Find the value formulas Geometry Given Hence hypotenuse included angle increases in absolute isosceles Law of Sines Leaving latitude leg is called loga logarithms loge longitude miles negative opposite leg places of decimals PLANE SAILING radians radius ratio regular polygon right triangle secant Sect SECTION ship sails sin-¹x sin(x sin² sin²x sine and cosine solution square chains subtended tan-¹ tan² tan²x tangent tower TRIGONOMETRIC FUNCTIONS Trigonometry unit circle Wentworth's x cos y yards
Popular passages
Page 53 - ... cos y + cos x sin 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 63 - The sides of a triangle are proportional to the sines of the opposite angles.
Page 25 - TRIANGLE 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 118 - 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 90 - 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.
Page 29 - From the top of a hill the angles of depression of two objects situated in the...
Page 53 - Formula [2], sin (x + y) _ sin x cos y + cos x sin y '
Page 86 - W., and after the ship had sailed 18 miles S. 67° 30' W. it bore N. 11° 15' E. Find its distance from each position of the ship. 2. Two objects, A and B, were observed from a ship to be at the same instant in a line bearing N. 15° E. The ship then sailed northwest 5 miles, when it was found that A bore due east and В bore northeast.
Page 65 - Ъ — sinA : sin 5; whence, by the Theory of Proportion, a — b _ sin A — sin B...
Page 68 - Two observers 5 miles apart on a plain, and facing each other, find that the angles of elevation of a balloon in the same vertical plane with themselves are 55° and 58°, respectively.