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Use a calculator to find the approximate value of the following expression if possible. Express your answers in radians and round to the hundredth. cos ¹(-2.5) 0.88 radians O 1.98 radians O 15.67 radians Impossible since the value is not in the domain of cos¹ (x).

Use a calculator to find the approximate value of the following expression if possible. Express your answers in radians and round to the hundredth. cos ¹(-2.5) 0.88 radians O 1.98 radians O 15.67 radians Impossible since the value is not in the domain of cos¹ (x).

Trigonometry (MindTap Course List)
Trigonometry (MindTap Course List)
8th Edition
ISBN:9781305652224
Author:Charles P. McKeague, Mark D. Turner
Publisher:Charles P. McKeague, Mark D. Turner
Chapter2: Right Triangle Trigonometry
Section: Chapter Questions
Problem 5GP
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**Finding the Approximate Value of the Expression Using a Calculator** In this exercise, you will use a calculator to find the approximate value of the following expression, if possible. Make sure to express your answers in radians and round to the nearest hundredth. **Exercise:** Calculate \(\cos^{-1}(-2.5)\) Options: 1. \(0.88\) radians 2. \(1.98\) radians 3. \(15.67\) radians 4. Impossible since the value is not in the domain of \(\cos^{-1}(x)\) Please note that the cosine inverse function \(\cos^{-1}(x)\) is only defined for values of \(x\) in the interval \([-1, 1]\). Therefore, it's essential to check if the given value, \(-2.5\), lies within this domain before attempting to find its inverse. **Analysis of Options:** 1. **0.88 radians**: This value falls within a valid range of the \(\cos^{-1}\) function if \(-2.5\) were indeed within its domain. However, note the domain first. 2. **1.98 radians**: Similar to the first option, it is essential to check the domain for eligibility. 3. **15.67 radians**: This value is highly unlikely as it exceeds the standard range of \(\cos^{-1}(x)\), which typically returns values between \(0\) and \(\pi\) radians. 4. **Impossible since the value is not in the domain of \(\cos^{-1}(x)\)**: This is the most mathematically accurate option since \(-2.5\) is clearly outside the valid range of \([-1, 1]\). Given the domain of the \(\cos^{-1}(x)\) function, it is clear that \(\cos^{-1}(-2.5)\) is impossible to calculate, as \(-2.5\) does not lie within the interval \([-1, 1]\). **Correct Answer:** *Impossible since the value is not in the domain of \(\cos^{-1}(x)\)*.
Transcribed Image Text:**Finding the Approximate Value of the Expression Using a Calculator** In this exercise, you will use a calculator to find the approximate value of the following expression, if possible. Make sure to express your answers in radians and round to the nearest hundredth. **Exercise:** Calculate \(\cos^{-1}(-2.5)\) Options: 1. \(0.88\) radians 2. \(1.98\) radians 3. \(15.67\) radians 4. Impossible since the value is not in the domain of \(\cos^{-1}(x)\) Please note that the cosine inverse function \(\cos^{-1}(x)\) is only defined for values of \(x\) in the interval \([-1, 1]\). Therefore, it's essential to check if the given value, \(-2.5\), lies within this domain before attempting to find its inverse. **Analysis of Options:** 1. **0.88 radians**: This value falls within a valid range of the \(\cos^{-1}\) function if \(-2.5\) were indeed within its domain. However, note the domain first. 2. **1.98 radians**: Similar to the first option, it is essential to check the domain for eligibility. 3. **15.67 radians**: This value is highly unlikely as it exceeds the standard range of \(\cos^{-1}(x)\), which typically returns values between \(0\) and \(\pi\) radians. 4. **Impossible since the value is not in the domain of \(\cos^{-1}(x)\)**: This is the most mathematically accurate option since \(-2.5\) is clearly outside the valid range of \([-1, 1]\). Given the domain of the \(\cos^{-1}(x)\) function, it is clear that \(\cos^{-1}(-2.5)\) is impossible to calculate, as \(-2.5\) does not lie within the interval \([-1, 1]\). **Correct Answer:** *Impossible since the value is not in the domain of \(\cos^{-1}(x)\)*.
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