Thinking Mathematically (6th Edition)

Published by Pearson
ISBN 10: 0321867327
ISBN 13: 978-0-32186-732-2

Chapter 10 - Geometry - 10.6 Right Triangle Trigonometry - Exercise Set 10.6 - Page 668: 61

Answer

Values of trigonometric ratio \[\text{Sine}\] or \[\text{cosine}\] can be equal to one, but cannot be greater than \[1\] as their values varies from \[0\] and\[1\]in the range of \[0{}^\circ \]to\[90{}^\circ \]and after this range.

Work Step by Step

The hypotenuse in a right angled triangle is bigger than the opposite side of the triangle. So, for the angles that are bigger than \[0{}^\circ \] but lesser than \[90{}^\circ \], the sine ratio will be lesser than\[1\]. For angles not lying within these limits, the \[\text{Sine}\]ratio can have the values ranging from\[-1\]to\[1\]. Thus, the values of the trigonometric functions cannot be greater than\[1\].
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