Volume 27, Issue 1, October 2016, Pages 216–224
Pankaj Tyagi1, Jyoti Sharma2, Kamal Ranjan3, Vikas Tomar4, and Raghavendra Tripath5
1 Cluster Innovation Centre, University of Delhi, Delhi-110007, India
2 Cluster Innovation Centre, University of Delhi, Delhi-110007, India
3 B. Tech. (IT & Mathematical Innovations), Cluster Innovation Centre, University of Delhi, Delhi-110007, India
4 B. Tech. (IT & Mathematical Innovations), Cluster Innovation Centre, University of Delhi, Delhi-110007, India
5 B. Tech. (IT & Mathematical Innovations), Cluster Innovation Centre, University of Delhi, Delhi-110007, India
Original language: English
Copyright © 2016 ISSR Journals. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Angles and lengths of a triangle engaged the mathematicians from historical time. The branch of mathematics that resulted from these studies is now known as Trigonometry. The discovery that lengths of a right angled triangle and the angles between them have a definite relationship led to the invention of trigonometric functions. The determination of values of various trigonometric functions like sine, cosine, tangent, cotangent, cosecant and secant for various angles in four quarters of a circle was a challenging task. Various methods and tables were generated for determining these values. Efforts were made to invent various devices for these measurements. There exist various U.S. patents [1-7] based on devices developed to visualize, teach and calculate values of various trigonometric functions. In the present paper, we are reporting a very accurate, economic, simple, and portable device designed for measuring the values of Trigonometric functions. The patent application number for the reported device is 1068/DEL/2015. The device consists of (i) a unit radius circular disc (with 360o angle scale indication on its circumference of 1o accuracy, X- and Y-linear scales markings with accuracy of 0.01 unit and marking of four quadrants of the circle), (ii) a corresponding linear scale with positive marking, (iii) a corresponding linear scale with negative marking and (iv) a blank transparent strip. The device can directly measure all the six trigonometric identities (sine, cosine, tangent, cotangent, cosecant and secant) for any value of angle up to the accuracy of 0.01 units just by measurement of only one parameter on one of the provided scale by appropriately placing it on Trig Disc along with blank linear strip in respective quadrants. Single measurement on a linear scale and no division or calculations of values is main feature of the device.
Author Keywords: Trigonometry, trigonometric functions, trigonometric function values, Trigonometric devices, trigonometric identities.
Pankaj Tyagi1, Jyoti Sharma2, Kamal Ranjan3, Vikas Tomar4, and Raghavendra Tripath5
1 Cluster Innovation Centre, University of Delhi, Delhi-110007, India
2 Cluster Innovation Centre, University of Delhi, Delhi-110007, India
3 B. Tech. (IT & Mathematical Innovations), Cluster Innovation Centre, University of Delhi, Delhi-110007, India
4 B. Tech. (IT & Mathematical Innovations), Cluster Innovation Centre, University of Delhi, Delhi-110007, India
5 B. Tech. (IT & Mathematical Innovations), Cluster Innovation Centre, University of Delhi, Delhi-110007, India
Original language: English
Copyright © 2016 ISSR Journals. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
Angles and lengths of a triangle engaged the mathematicians from historical time. The branch of mathematics that resulted from these studies is now known as Trigonometry. The discovery that lengths of a right angled triangle and the angles between them have a definite relationship led to the invention of trigonometric functions. The determination of values of various trigonometric functions like sine, cosine, tangent, cotangent, cosecant and secant for various angles in four quarters of a circle was a challenging task. Various methods and tables were generated for determining these values. Efforts were made to invent various devices for these measurements. There exist various U.S. patents [1-7] based on devices developed to visualize, teach and calculate values of various trigonometric functions. In the present paper, we are reporting a very accurate, economic, simple, and portable device designed for measuring the values of Trigonometric functions. The patent application number for the reported device is 1068/DEL/2015. The device consists of (i) a unit radius circular disc (with 360o angle scale indication on its circumference of 1o accuracy, X- and Y-linear scales markings with accuracy of 0.01 unit and marking of four quadrants of the circle), (ii) a corresponding linear scale with positive marking, (iii) a corresponding linear scale with negative marking and (iv) a blank transparent strip. The device can directly measure all the six trigonometric identities (sine, cosine, tangent, cotangent, cosecant and secant) for any value of angle up to the accuracy of 0.01 units just by measurement of only one parameter on one of the provided scale by appropriately placing it on Trig Disc along with blank linear strip in respective quadrants. Single measurement on a linear scale and no division or calculations of values is main feature of the device.
Author Keywords: Trigonometry, trigonometric functions, trigonometric function values, Trigonometric devices, trigonometric identities.
How to Cite this Article
Pankaj Tyagi, Jyoti Sharma, Kamal Ranjan, Vikas Tomar, and Raghavendra Tripath, “Trig-Disc: An innovative device for determination of values of trigonometric functions with single measurement,” International Journal of Innovation and Scientific Research, vol. 27, no. 1, pp. 216–224, October 2016.
