Difference between revisions of "2006 AMC 12A Problems/Problem 15"
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== Solution == | == Solution == | ||
| + | *For <math>\cos x = 0</math>, x must be in the form of <math>\frac{\pi}{2} + \pi n</math>, where <math>n</math> denotes any [[integer]]. | ||
| + | *For <math>\cos (x+z) = 1 / 2</math>, <math>x + z = \frac{\pi}{3} +2\pi n, \frac{5\pi}{3} + 2\pi n</math>. | ||
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| + | <!-- explanation needed-->The smallest possible value of <math>z</math> will be that of <math>\frac{5\pi}{3} - \frac{3\pi}{2} = \frac{\pi}{6} \Rightarrow A</math>. | ||
== See also == | == See also == | ||
* [[2006 AMC 12A Problems]] | * [[2006 AMC 12A Problems]] | ||
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| − | + | {{AMC box|year=2006|n=12A|num-b=14|num-a=16}} | |
[[Category:Introductory Algebra Problems]] | [[Category:Introductory Algebra Problems]] | ||
Revision as of 20:11, 31 January 2007
Problem
Suppose 
and 
. What is the smallest possible positive value of 
?
Solution
- For
, x must be in the form of 
, where 
denotes any integer. - For
, 
.
, x must be in the form of 
, where 
denotes any 
, 
.The smallest possible value of will be that of 
.
See also
| {{{header}}} | ||
| Preceded by Problem 14 |
AMC 12A 2006 |
Followed by Problem 16 |
