Difference between revisions of "008A Sample Final A, Question 19"
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(Created page with "'''Question: ''' Compute <math>\arcsin -\frac{\sqrt{3}}{2}</math>. Provide your answer in radians. {| class="mw-collapsible mw-collapsed" style = "text-align:left;" !Foundat...") |
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|1) What is the range of <math>\arcsin </math>? | |1) What is the range of <math>\arcsin </math>? | ||
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|Since the range of <math>\arcsin </math> is <math> [-\frac{\pi}{2}, \frac{\pi}{2}]</math>, the answer must be in that range. | |Since the range of <math>\arcsin </math> is <math> [-\frac{\pi}{2}, \frac{\pi}{2}]</math>, the answer must be in that range. | ||
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|<math>\arcsin -\frac{\sqrt{3}}{2} = - \frac{\pi}{3}</math> | |<math>\arcsin -\frac{\sqrt{3}}{2} = - \frac{\pi}{3}</math> | ||
Latest revision as of 00:04, 26 May 2015
Question: Compute Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \arcsin -\frac{\sqrt{3}}{2}} . Provide your answer in radians.
| Foundations: | |
|---|---|
| 1) What is the range of Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \arcsin } ? | |
| 2) Sine of what angle in the range of Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \arcsin} yields Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle -\frac{\sqrt{3}}{2}} ? | Answer: |
| 1) The range of arcsin is Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle [-\frac{\pi}{2}, \frac{\pi}{2}]} . | |
| 2) Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \sin( -\frac{\pi}{3} ) = -\frac{\sqrt{3}}{2}} . |
Solution:
| Step 1: |
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| Since the range of Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \arcsin } is Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle [-\frac{\pi}{2}, \frac{\pi}{2}]} , the answer must be in that range. |
| Final Answer: |
|---|
| Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \arcsin -\frac{\sqrt{3}}{2} = - \frac{\pi}{3}} |