005 Sample Final A, Question 13 - Revision history

Matt Lee at 03:58, 22 May 2015

2015-05-22T03:58:30Z

Kayla Murray at 22:59, 19 May 2015

2015-05-19T22:59:55Z

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

2015-05-01T04:20:24Z

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..."

New page

''' 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;"
! Final Answers
|-
|a) False. Nothing in the definition of a geometric sequence requires the common ratio to be always positive. For example, <math>a_n = (-a)^n</math>
|-
|b) False. Linear systems only have a solution if the lines intersect. So y = x and y = x + 1 will never intersect because they are parallel.
|-
|c) False. <math>y = x^2</math> does not have an inverse.
|-
|d) True. <math>cos^2(x) - cos(x) = 0</math> has multiple solutions.
|-
|e) True.
|-
|f) False.
|}

← Older revision		Revision as of 03:58, 22 May 2015
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	''' Question ''' Give the exact value of the following if its defined, otherwise, write undefined. <br>		''' 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>		<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>
		+	\|}
		+

@@ Line 4: / Line 4: @@
 {| class="mw-collapsible mw-collapsed" style = "text-align:left;"
-! Final Answers
+! Step 1:
 |-
-|a) False. Nothing in the definition of a geometric sequence requires the common ratio to be always positive. For example, <math>a_n = (-a)^n</math>
+| 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
 |-
-|b) False. Linear systems only have a solution if the lines intersect. So y = x and y = x + 1 will never intersect because they are parallel.
+|for <math>\sin(\theta)=2</math>. So, <math>\sin^{-1}(2)</math> is undefined.
 |-
-|c) False. <math>y = x^2</math> does not have an inverse.
+| 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
 |-
-|d) True. <math>cos^2(x) - cos(x) = 0</math> has multiple solutions.
+|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>.
 |-
-|e) True.
+| 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
 |-
-|f) False.
+|reference angle <math>\frac{7\pi}{6}</math>. Since <math>\cos\left(\frac{7\pi}{6}\right)=\frac{-\sqrt{3}}{2}</math>, we have
 |}

005 Sample Final A, Question 13 - Revision history

Matt Lee at 03:58, 22 May 2015

Kayla Murray at 22:59, 19 May 2015

Matt Lee: 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..."

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