MathAdmin: Created page with "''' Question ''' Give the exact value of the following if its defined, otherwise, write undefined.
$(a) \sin^{-1}(2) \qquad \qquad (b) \sin\left(\frac{-32\pi}{3}\ri..."$

2015-06-01T01:27:40Z

Created page with "''' Question ''' Give the exact value of the following if its defined, otherwise, write undefined. <br> <math>(a) \sin^{-1}(2) \qquad \qquad (b) \sin\left(\frac{-32\pi}{3}\ri..."

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''' Question ''' Give the exact value of the following if its defined, otherwise, write undefined. <br>
<math>(a) \sin^{-1}(2) \qquad \qquad (b) \sin\left(\frac{-32\pi}{3}\right) \qquad \qquad (c)\sec\left(\frac{-17\pi}{6}\right)</math>

{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
! Foundations:
|-
|1) What is the domain of <math>\sin^{-1}?</math>
|-
|2) What are the reference angles for <math>\frac{-32\pi}{3}</math> and <math>\frac{-17\pi}{6}</math>?
|-
|Answers:
|-
|1) The domain is <math>[-1, 1].</math>
|-
|2) The reference angle for <math>\frac{-32\pi}{3}</math> is <math>\frac{4\pi}{3}</math>, and the reference angle for <math>\frac{-17\pi}{6}</math> is <math>\frac{7\pi}{6}</math>
|}

{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
! Step 1:
|-
| For (a), we want an angle <math>\theta</math> such that <math>\sin(\theta)=2</math>. Since <math>-1\leq \sin (\theta)\leq 1</math>, it is impossible
|-
|for <math>\sin(\theta)=2</math>. So, <math>\sin^{-1}(2)</math> is undefined.
|}

{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
! Step 2:
|-
| For (b), we need to find the reference angle for <math>\frac{-32\pi}{3}</math>. If we add multiples of <math>2\pi</math> to this angle, we get the
|-
|reference angle <math>\frac{4\pi}{3}</math>. So, <math>\sin\left(\frac{-32\pi}{3}\right)=\sin\left(\frac{4\pi}{3}\right)=\frac{-\sqrt{3}}{2}</math>.
|}

{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
! Step 3:
|-
| For (c), we need to find the reference angle for <math>\frac{-17\pi}{6}</math>. If we add multiples of <math>2\pi</math> to this angle, we get the
|-
|reference angle <math>\frac{7\pi}{6}</math>. Since <math>\cos\left(\frac{7\pi}{6}\right)=\frac{-\sqrt{3}}{2}</math>, we have
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|<math>\sec\left(\frac{-17\pi}{6}\right)=\sec\left(\frac{7\pi}{6}\right)=\frac{2}{-\sqrt{3}}=\frac{-2\sqrt{3}}{3}</math>.
|}

{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
! Final Answer:
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|a) undefined
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|b) <math>\frac{-\sqrt{3}}{2}</math>
|-
|c)<math>\frac{-2\sqrt{3}}{3}</math>
|}

[[005 Sample Final A|'''<u>Return to Sample Exam</u>''']]

005 Sample Final A, Question 13 - Revision history

MathAdmin: Created page with "''' Question ''' Give the exact value of the following if its defined, otherwise, write undefined. (a) \sin^{-1}(2) \qquad \qquad (b) \sin\left(\frac{-32\pi}{3}\ri..."

MathAdmin: Created page with "''' Question ''' Give the exact value of the following if its defined, otherwise, write undefined.
$(a) \sin^{-1}(2) \qquad \qquad (b) \sin\left(\frac{-32\pi}{3}\ri..."$