Chapter 13 - The Trigonometric Functions - 13.1 Definitions of the Trigonometric Functions - 13.1 Exercises - Page 678: 25

$$\tan {30^ \circ } = \frac{{\sqrt 3 }}{3},\,\,\,\,\cot {30^ \circ } = \sqrt 3 ,\,\,\,\,\,\csc {30^ \circ } = 2$$

Work Step by Step

\eqalign{ & {\text{from the table we have the following information}} \cr & \sin {30^ \circ } = \frac{1}{2}{\text{, }}\cos {30^ \circ } = \frac{{\sqrt 3 }}{2}{\text{ and }}\sec {30^ \circ } = \frac{{2\sqrt 3 }}{3} \cr & {\text{then}}{\text{, using the elementary trigonometric identities we obtain}} \cr & \tan {30^ \circ } = \frac{{\sin {{30}^ \circ }}}{{\cos {{30}^ \circ }}} = \frac{{1/2}}{{\sqrt 3 /2}} = \frac{1}{{\sqrt 3 }} = \frac{{\sqrt 3 }}{3} \cr & \cot {30^ \circ } = \frac{1}{{\tan {{30}^ \circ }}} = \frac{1}{{\sqrt 3 /3}} = \sqrt 3 \cr & \csc {30^ \circ } = \frac{1}{{\sin {{30}^ \circ }}} = \frac{1}{{1/2}} = 2 \cr}

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