Difference between revisions of "8A F11 Q17"
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(Created page with "'''Question: ''' Compute the following trig ratios: a) <math> \sec \frac{3\pi}{4}</math> b) <math> \tan \frac{11\pi}{6}</math> c) <m...") |
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|2) a) Quadrant 2, b) Quadrant 4, c) Quadrant 3. The reference angles are: <math> \frac{\pi}{4}, \frac{\pi}{6}</math>, and 60 degrees or <math>\frac{\pi}{3}</math> | |2) a) Quadrant 2, b) Quadrant 4, c) Quadrant 3. The reference angles are: <math> \frac{\pi}{4}, \frac{\pi}{6}</math>, and 60 degrees or <math>\frac{\pi}{3}</math> | ||
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Solution: | Solution: | ||
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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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| + | [[8AF11Final|<u>'''Return to Sample Exam</u>''']] | ||
Latest revision as of 15:01, 6 April 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 | |
|---|---|
| 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: |
|---|
| 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}} |