Find the exact value of each of the following. No decimals. b) cos (-)()c) tan4 f) csc2.

Name: Find the exact value of each of the following. No decimals. b) cos (-)
Uploaded: 2024-03-20T07:06:41.000Z
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Description: Find the exact value of each of the following. No decimals. b) cos (-)()c) tan4 f) csc2.

Given : b) cos-5π4c) tanπ2f) csc-π2

Answered: b) cos (-) c) tan ()

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter7: Analytic Trigonometry

Section7.3: The Addition And Subtraction Formulas

Problem 54E

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Find the exact value of each of the following. No decimals.

Expert Solution

Step 1 : Analysis

Given :

$b) \cos (- \frac{5 π}{4}) c) \tan (\frac{π}{2}) f) \csc (- \frac{π}{2})$

Step 2 : Simplification

Using $\cos (- θ) = \cos θ$ ,

$\cos (- \frac{5 π}{4}) = \cos (\frac{5 π}{4})$

Using $\cos (π + θ) = - \cos θ$ ,

$\begin{array}{rcl} \cos (\frac{5 π}{4}) & = & \cos (π + \frac{π}{4}) \\ \cos (\frac{5 π}{4}) & = & - \cos (\frac{π}{4}) \\ \cos (\frac{5 π}{4}) & = & - \frac{\sqrt{2}}{2} \end{array}$

Therefore

$\begin{array}{rcl} \cos \end{array} \begin{array}{rcl} (- \frac{5 π}{4}) \end{array} \begin{array}{rcl} \end{array} \begin{array}{rcl} = \end{array} \begin{array}{rcl} \end{array} \begin{array}{rcl} - \end{array} \begin{array}{rcl} \frac{\sqrt{2}}{2} \end{array}$

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