Difference between revisions of "008A Sample Final A, Question 17"
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|1) How is secant related to either sine or cosine? | |1) How is secant related to either sine or cosine? | ||
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| − | ! Final Answer A: | + | !Final Answer A: |
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|Since <math> \sec(x) = \frac{1}{\cos(x)} </math>, and the angle is in quadrant 2, <math> \sec(\frac{3\pi}{4}) = \frac{1}{\cos(\frac{3\pi}{4})} = \frac{1}{\frac{-1}{\sqrt{2}}} = -\sqrt{2}</math> | |Since <math> \sec(x) = \frac{1}{\cos(x)} </math>, and the angle is in quadrant 2, <math> \sec(\frac{3\pi}{4}) = \frac{1}{\cos(\frac{3\pi}{4})} = \frac{1}{\frac{-1}{\sqrt{2}}} = -\sqrt{2}</math> | ||
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| − | ! Final Answer B: | + | !Final Answer B: |
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|The reference angle is <math> \frac{\pi}{6} </math> and is in the fourth quadrant. So tangent will be negative. Since the angle is 30 degees, using the 30-60-90 right triangle, we can conclude that <math>\tan(\frac{11\pi}{6}) = -\frac{\sqrt{3}}{3}</math> | |The reference angle is <math> \frac{\pi}{6} </math> and is in the fourth quadrant. So tangent will be negative. Since the angle is 30 degees, using the 30-60-90 right triangle, we can conclude that <math>\tan(\frac{11\pi}{6}) = -\frac{\sqrt{3}}{3}</math> | ||
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| − | ! Final Answer C: | + | !Final Answer C: |
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| − | |Sin(-120) = - sin(120). So you can either compute sin(120) or sin(-120) = sin(240). Since the reference angle is 60 degrees, or <math>\frac{\pi}{3}</math>, So <math> sin(-120) = \frac{\sqrt{3}}{2}</math> | + | |Sin(-120) = - sin(120). So you can either compute sin(120) or sin(-120) = sin(240). Since the reference angle is 60 degrees, or <math>\frac{\pi}{3}</math> , So <math> \sin(-120) = \frac{\sqrt{3}}{2}</math> |
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[[008A Sample Final A|<u>'''Return to Sample Exam</u>''']] | [[008A Sample Final A|<u>'''Return to Sample Exam</u>''']] | ||
Latest revision as of 23:03, 25 May 2015
Question: Compute the following trig ratios: a) 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 \sec \frac{3\pi}{4}} b) 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 \tan \frac{11\pi}{6}} c) 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(-120)}
| Foundations: | |
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| 1) How is secant related to either sine or cosine? | |
| 2) What quadrant is each angle in? What is the reference angle for each? | Answer: |
| 1) 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 \sec(x) = \frac{1}{\cos(x)}} | |
| 2) a) Quadrant 2, b) Quadrant 4, c) Quadrant 3. The reference angles are: 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}{4}, \frac{\pi}{6}} , and 60 degrees or 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}{3}} |
Solution:
| Final Answer A: |
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| Since 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 \sec(x) = \frac{1}{\cos(x)} } , and the angle is in quadrant 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 \sec(\frac{3\pi}{4}) = \frac{1}{\cos(\frac{3\pi}{4})} = \frac{1}{\frac{-1}{\sqrt{2}}} = -\sqrt{2}} |
| Final Answer B: |
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| The reference angle 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}{6} } and is in the fourth quadrant. So tangent will be negative. Since the angle is 30 degees, using the 30-60-90 right triangle, we can conclude that 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 \tan(\frac{11\pi}{6}) = -\frac{\sqrt{3}}{3}} |
| Final Answer C: |
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| Sin(-120) = - sin(120). So you can either compute sin(120) or sin(-120) = sin(240). Since the reference angle is 60 degrees, or 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}{3}} , So 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(-120) = \frac{\sqrt{3}}{2}} |