Q. 47 Find the exact values of the six... [FREE SOLUTION]

91影视

Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 6: Q. 47 (page 381)

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.
$\frac{2 蟺}{3}$

Short Answer

Expert verified

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

Step by step solution

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

The given angle is $\frac{2 蟺}{3}$ . This angle is multiple of $\frac{蟺}{3}$ .

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

Step 2. Determine the exact value of sine function.

The exact value of the sine function is:

$\sin (\frac{2 蟺}{3}) = y \sin (\frac{2 蟺}{3}) = \frac{\sqrt{3}}{2}$

Step 3. Determine the exact value of cosine function.

The exact value of the cosine function is:

$\cos (\frac{2 蟺}{3}) = x \cos (\frac{2 蟺}{3}) = - \frac{1}{2}$

Step 4. Determine the exact value of tangent function.

The exact value of the tangent function is:

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

Step 5. Determine the exact value of cosecant function.

The exact value of the cosecant function is:

\begin{array}{rcl} \csc 胃 & = & \frac{1}{\sin 胃} \\ \csc (\frac{2 蟺}{3}) & = & \frac{1}{\frac{\sqrt{3}}{2}} \\ \csc (\frac{2 蟺}{3}) & = & \frac{2}{\sqrt{3}} \end{array}

Step 6. Determine the exact value of secant function.

The exact value of the secant function is:

$\begin{array}{rcl} \sec 胃 & = & \frac{1}{\cos 胃} \\ \sec (\frac{2 蟺}{3}) & = & \frac{1}{\frac{- 1}{2}} \\ \sec (\frac{2 蟺}{3}) & = & - 2 \end{array}$

Step 7. Determine the exact value of cotangent function.

The exact value of the cotangent function is:

\begin{array}{rcl} \cot 胃 & = & \frac{1}{\tan 胃} \\ \cot (\frac{2 蟺}{3}) & = & \frac{1}{- \sqrt{3}} \\ \cot (\frac{2 蟺}{3}) & = & - \frac{1}{\sqrt{3}} \end{array}

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91影视

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.
$\frac{2 蟺}{3}$

Short Answer

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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91影视

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.2蟺3

Short Answer

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.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Decision Maths

Probability and Statistics

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Statistics

Calculus

Study anywhere. Anytime. Across all devices.

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.
$\frac{2 蟺}{3}$