Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 5 - Section 5.2 - Trigonometric Functions of Real Numbers - 5.2 Exercises - Page 417: 26

Answer

$sin(\frac{3\pi}{2}) = -1$ $cos(\frac{3\pi}{2}) = 0$ $tan(\frac{3\pi}{2}) = undefined$ $csc(\frac{3\pi}{2}) = -1$ $sec(\frac{3\pi}{2}) = undefined$ $cot(\frac{3\pi}{2}) = 0$ \begin{bmatrix} t & sin \space t & cos \space t & tan \space t & csc \space t & sec \space t & cot \space t \\ 0 & 0 & 1 & 0 & undef. & 1 & undef. \\ \frac {\pi} 2 & 1 & 0& undef. & 1 & undef. & 0\\ \pi & 0 & -1 & 0 & undef. & -1 & undef.\\ \frac{3\pi}{2} & -1 & 0 & undef. & -1 & undef. & 0 \end{bmatrix}

Work Step by Step

1. Find a Reference Number. $t^- = \frac{3\pi}2 - \pi = \frac{\pi} 2$ 2. See Table 1 (Page 410), it contains all the values for the trigonometric functions when $t = \pi/2$. $sin(\frac{\pi}{2}) = 1$ $cos(\frac{\pi}{2}) = 0$ $tan(\frac{\pi}{2}) = undefined$ $csc(\frac{\pi}{2}) = 1$ $sec(\frac{\pi}{2}) = undefined$ $cot(\frac{\pi}{2}) = 0$ 3. Since $3\pi/2$ is in Quadrant III, sin($3\pi/2$) and csc($3\pi/2$) are negative. $sin(\frac{3\pi}{2}) = -1$ $cos(\frac{3\pi}{2}) = 0$ $tan(\frac{3\pi}{2}) = undefined$ $csc(\frac{3\pi}{2}) = -1$ $sec(\frac{3\pi}{2}) = undefined$ $cot(\frac{3\pi}{2}) = 0$ 4. Completing the Table: \begin{bmatrix} t & sin \space t & cos \space t & tan \space t & csc \space t & sec \space t & cot \space t \\ 0 & 0 & 1 & 0 & undef. & 1 & undef. \\ \frac {\pi} 2 & 1 & 0& undef. & 1 & undef. & 0\\ \pi & 0 & -1 & 0 & undef. & -1 & undef.\\ \frac{3\pi}{2} & -1 & 0 & undef. & -1 & undef. & 0 \end{bmatrix}
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