Book edition 6th

Author(s) Sullivan

Pages 1200 pages

ISBN 9780321795465

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Short Answer

Find the exact values of the six trigonometric functions of the given angle. If any are not defined, say "not defined." Do not use a calculator.
$210 °$

The exact values of the six trigonometric functions are $\sin (210 °) = - \frac{1}{2}$ , $\cos (210 °) = - \frac{\sqrt{3}}{2}$ , $\tan (210 °) = \frac{1}{\sqrt{3}}$ , $\csc (210 °) = - 2$ , $\sec (210 °) = - \frac{2}{\sqrt{3}}$ and $\cot (210 °) = \sqrt{3}$ .

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Determine a point corresponds to the given angle.

The given angle is $210 ° = \frac{7 π}{6}$ . This angle is multiple of $\frac{π}{6}$ .

From the below figure, we see the point $(- \frac{\sqrt{3}}{2}, - \frac{1}{2})$ corresponds to $210 °$ .

Step 2. Determine the exact value of sine function.

The exact value of the sine function is:

$\sin (210 °) = y \sin (210 °) = - \frac{1}{2}$

Step 3. Determine the exact value of cosine function.

The exact value of the cosine function is:

$\cos (210 °) = x \cos (210 °) = - \frac{\sqrt{3}}{2}$

Step 4. Determine the exact value of tangent function.

The exact value of the tangent function is:

$\begin{array}{rcl} \tan θ & = & \frac{\sin θ}{\cos θ} \\ \tan (210 °) & = & \frac{- \frac{1}{2}}{- \frac{\sqrt{3}}{2}} \\ \tan (210 °) & = & \frac{1}{\sqrt{3}} \end{array}$

Step 5. Determine the exact value of cosecant function.

The exact value of the cosecant function is:

$\begin{array}{rcl} \csc θ & = & \frac{1}{\sin θ} \\ \csc (210 °) & = & \frac{1}{- \frac{1}{2}} \\ \csc (210 °) & = & - 2 \end{array}$

Step 6. Determine the exact value of secant function.

The exact value of the secant function is:

$\begin{array}{rcl} \sec θ & = & \frac{1}{\cos θ} \\ \sec (210 °) & = & \frac{1}{\frac{- \sqrt{3}}{2}} \\ \sec (210 °) & = & - \frac{2}{\sqrt{3}} \end{array}$

Step 7. Determine the exact value of cotangent function.

The exact value of the cotangent function is:

$\begin{array}{rcl} \cot θ & = & \frac{1}{\tan θ} \\ \cot (210 °) & = & \frac{1}{\frac{1}{\sqrt{3}}} \\ \cot (210 °) & = & \sqrt{3} \end{array}$

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Precalculus Enhanced with Graphing Utilities

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Short Answer

Find the exact values of the six trigonometric functions of the given angle. If any are not defined, say "not defined." Do not use a calculator.
$210 °$

Step by Step Solution

Step 1. Determine a point corresponds to the given angle.

Step 2. Determine the exact value of sine function.

Step 3. Determine the exact value of cosine function.

Step 4. Determine the exact value of tangent function.

Step 5. Determine the exact value of cosecant function.

Step 6. Determine the exact value of secant function.

Step 7. Determine the exact value of cotangent function.

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Precalculus Enhanced with Graphing Utilities

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Short Answer

Find the exact values of the six trigonometric functions of the given angle. If any are not defined, say "not defined." Do not use a calculator.210°

Step by Step Solution

Step 1. Determine a point corresponds to the given angle.

Step 2. Determine the exact value of sine function.

Step 3. Determine the exact value of cosine function.

Step 4. Determine the exact value of tangent function.

Step 5. Determine the exact value of cosecant function.

Step 6. Determine the exact value of secant function.

Step 7. Determine the exact value of cotangent function.

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Find the exact values of the six trigonometric functions of the given angle. If any are not defined, say "not defined." Do not use a calculator.
$210 °$