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MATHS

MATHS. P R O J E C T. KEY FOR TRIGONOMETRIC FUNCTIONS. INTRODUCTION ANGLES DEGREE MEASURE RADIAN FORMULAS. INTRODUCTION. THE WORD TRIGONOMETRY IS DERIVED FROM THE GREEK WORDS TRIGON AND METRON AND IT MEANS MEASURING THE SIDES OF A TRIANGLE.

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MATHS

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  1. MATHS P R O J E C T

  2. KEY FOR TRIGONOMETRIC FUNCTIONS • INTRODUCTION • ANGLES • DEGREE MEASURE • RADIAN • FORMULAS

  3. INTRODUCTION THE WORD TRIGONOMETRY IS DERIVED FROM THE GREEK WORDS TRIGON AND METRON AND IT MEANS MEASURING THE SIDES OF A TRIANGLE. THE SUBJECT WAS ORIGINALLY DEVELOPED TO SOLVE GEOMETRIC PROBLEMS INVOLVING TRIANGLES. CURRENTLY TRIGONOMETRY IS USED IN MANY AREAS SUCH AS DESIGNING ELECTRICAL CIRCUITS ,DESCRIBING THE STATE OF AN ATOM,PREDICTING THE HEIGHTS OF TIDES IN OCEAN AND IN MANY OTHER AREAS. HOME

  4. Angles Measuring angles Units HOME

  5. Measuring Angle • The value of θ thus defined is independent of the size of the circle: if the length of the radius is changed then the arc length changes in the same proportion, so the ratio s/r is unaltered. • In many geometrical situations, angles that differ by an exact multiple of a full circle are effectively equivalent (it makes no difference how many times a line is rotated through a full circle because it always ends up in the same place). However, this is not always the case. For example, when tracing a curve such as a spiral using polar coordinates, an extra full turn gives rise to a quite different point on the curve. Angles HOME

  6. Units • Angles are considered dimensionless, since they are defined as the ratio of lengths. • With the notable exception of the radian, most units of angular measurement are defined such that one full circle (i.e. one revolution) is equal to n units, for some whole number n (for example, in the case of degrees, n = 360). This is equivalent to setting k = n/2π in the formula above. (To see why, note that one full circle corresponds to an arc equal in length to the circle's circumference, which is 2πr, so s = 2πr. Substituting, we get θ = ks/r = 2πk. But if one complete circle is to have a numerical angular value of n, then we need θ = n. This is achieved by setting k = n/2π.) HOME Angles

  7. Degree Measure • The degree, denoted by a small superscript circle (°) is 1/360 of a full circle, so one full circle is 360°. One advantage of this old sexagesimal subunit is that many angles common in simple geometry are measured as a whole number of degrees. (The problem of having all "interesting" angles measured as whole numbers is of course insolvable.) Fractions of a degree may be written in normal decimal notation (e.g. 3.5° for three and a half degrees), but the following sexagesimal subunits of the "degree-minute-second" system are also in use, especially for geographical coordinates and in astronomy and ballistics: θ = s/r rad = 1 rad. Angles HOME

  8. Radian • The radian is the angle subtended by an arc of a circle that has the same length as the circle's radius (k = 1 in the formula given earlier). One full circle is 2π radians, and one radian is 180/π degrees, or about 57.2958 degrees. The radian is abbreviated rad, though this symbol is often omitted in mathematical texts, where radians are assumed unless specified otherwise. The radian is used in virtually all mathematical work beyond simple practical geometry, due, for example, to the pleasing and "natural" properties that the trigonometric functions display when their arguments are in radians. The radian is the (derived) unit of angular measurement in the SI system

  9. In order to measure an angle θ, a circular arc centered at the vertex of the angle is drawn, e.g. with a pair of compasses. The length of the arc s is then divided by the radius of the circle r, and possibly multiplied by a scaling constant k (which depends on the units of measurement that are chosen): • The value of thus defined is independent of the size of the circle: if the length of the radius is changed then the arc length changes in the same proportion, so the ratio s/r is unaltered. HOME

  10. FORMULAS • sin (x + y) =sin x cos y + cos x sin y • sin (x – y) =sin x cos y – cos x sin y • cos (x + y) =cos x cos y – sin x sin y • cos (x – y) =cos x cos y + sin x sin y

  11. sin(π/2 –x) = cos x • sin (π/2+x) = cos x • cos(π/2 –x) = sin x • cos (π/2+x) = – sin x

  12. ThanK YoU • Made By:- Abhinav, Shilpa Dipali, Sadhana Class-XI A

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