Technology & Engineering

Circular Functions

Circular functions are mathematical functions that are defined using the unit circle. The most common circular functions are the sine and cosine functions, which represent the y and x coordinates of points on the unit circle, respectively. These functions are widely used in technology and engineering for modeling periodic phenomena such as sound waves, alternating currents, and oscillations.

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  • Science and Mathematics for Engineering
    eBook - ePub

    Science and Mathematics for Engineering

    • John Bird(Author)
    • 2019(Publication Date)
    • Routledge
      (Publisher)
    Chapter 11 Introduction to trigonometry
    Why it is important to understand: Introduction to trigonometry
    Knowledge of angles and triangles is very important in engineering. Trigonometry is needed in surveying and architecture, for building structures/systems, designing bridges and solving scientific problems. Trigonometry is also used in electrical engineering: the functions that relate angles and side lengths in right angled triangles are useful in expressing how a.c. electric current varies with time. Engineers use triangles to determine how much force it will take to move along an incline, GPS satellite receivers use triangles to determine exactly where they are in relation to satellites orbiting hundreds of miles away. Whether you want to build a skateboard ramp, a stairway, or a bridge, you can’t escape trigonometry.
    At the end of this chapter, you should be able to:
    • state the theorem of Pythagoras and use it to find the unknown side of a right angled triangle
    • define sine, cosine and tangent of an angle in a right angled triangle
    • evaluate trigonometric ratios of angles
    • solve right angled triangles
    • sketch sine, cosine and tangent waveforms
    • state and use the sine rule
    • state and use the cosine rule
    • use various formulae to determine the area of any triangle
    • apply the sine and cosine rules to solving practical trigonometric problems

    11.1   Introduction

    Trigonometry is a subject that involves the measurement of sides and angles of triangles and their relationship with each other. There are many applications in engineering and science where a knowledge of trigonometry is needed.

    11.2   The theorem of Pythagoras

    The theorem of Pythagoras * states:
    ‘In any right-angled triangle, the square on the hypotenuse is equal to the sum of the squares on the other two sides.’ Science and Mathematics for Engineering. 978-0-367-20475-4, © John Bird. Published by Taylor & Francis. All rights reserved.
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