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Unit 4 Section 1 and 2

# Unit 4 Section 1 and 2 - UNIT 4 CIRCULAR AND TRIGONOMETRIC...

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UNIT 4. CIRCULAR AND TRIGONOMETRIC FUNCTIONS Trigonometry is the branch of mathematics concerned with the measurement of the parts, sides, and angles of a triangle. Plane trigonometry , which is the topic of this book, is restricted to triangles lying in a plane. Trigonometry is based on certain ratios, called trigonometric functions . On the other hand, circular functions are very similar to trigonometric functions and they use the same function names. While trigonometric functions are mappings from angle measurements of a triangle to the set of real numbers, circular functions are mappings from arc lengths of a unit circle to the set of numbers. It would be evident later on that these angle measurements and arc lengths are numerically equivalent. The early applications of the circular and trigonometric functions were to surveying, navigation, and engineering. These functions also play an important role in the study of all sorts of vibratory phenomena sound, light, electricity, etc. As a consequence, a considerable portion of the subject matter is concerned with a study of the properties of and relations among the circular and trigonometric functions. 4.1 THE UNIT CIRCLE Definition 4.1.1 A unit circle is a circle whose radius is equal to one unit and whose center is at the origin. Every point on the unit circle satisfies the equation Also, let be the set of all points on the unit circle, that is . The Unit Circle Let's pick a point on the circle. We'll choose a point where the is . If the is , what is the value? Solution: Using the equation of the unit circle, and by substitution, we have

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You can see there are two values. They can be found by putting into the equation for and solving for . Now, for us to look at the relationship between circular and trigonometric functions, let us have a brief discussion of the basic elements involve with this functions: angles and arcs. ANGLES
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Unit 4 Section 1 and 2 - UNIT 4 CIRCULAR AND TRIGONOMETRIC...

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