anonymous
  • anonymous
If sine of x equals 1 over 2, what is cos(x) and tan(x)? Explain your steps in complete sentences.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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jim_thompson5910
  • jim_thompson5910
Hint: Pythagorean Trig Identity \[\Large \sin^2(x) + \cos^2(x) = 1\]
anonymous
  • anonymous
Ok, so how would I continue off that? May you guide me through the problem please?
jim_thompson5910
  • jim_thompson5910
since sine is 1/2, squaring that gives you 1/4 you can replace all of sin^2 with 1/4 like this \[\Large \sin^2(x) + \cos^2(x) = 1\] \[\Large \frac{1}{4} + \cos^2(x) = 1\]

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jim_thompson5910
  • jim_thompson5910
now isolate cos(x)
anonymous
  • anonymous
we subract 1/4 from both sides
anonymous
  • anonymous
so now we square root both sides right?
jim_thompson5910
  • jim_thompson5910
correct on both statements
anonymous
  • anonymous
then how do we get tangent
jim_thompson5910
  • jim_thompson5910
\[\Large \tan(x) = \frac{\sin(x)}{\cos(x)}\]
anonymous
  • anonymous
Ok, hold on. Let me put everything together.
anonymous
  • anonymous
cos(x) = \[\sqrt{.75}\] is that how it should be written
jim_thompson5910
  • jim_thompson5910
or \[\Large \sqrt{\frac{3}{4}} = \frac{\sqrt{3}}{\sqrt{4}} = \frac{\sqrt{3}}{2}\]
jim_thompson5910
  • jim_thompson5910
most books I've seen use \[\Large \frac{\sqrt{3}}{2}\]
anonymous
  • anonymous
oh ok, so \[\tan(x) = \frac{ 1 }{ 2 } /\frac{ \sqrt{3} }{ 2 }\]
jim_thompson5910
  • jim_thompson5910
Yes correct. Now simplify
anonymous
  • anonymous
How would I do that?
jim_thompson5910
  • jim_thompson5910
|dw:1439850551781:dw|
jim_thompson5910
  • jim_thompson5910
|dw:1439850577166:dw|
anonymous
  • anonymous
so the answer is \[\frac{ 1 }{ \sqrt{3} }\]
jim_thompson5910
  • jim_thompson5910
rationalizing the denominator makes that turn into \[\Large \frac{\sqrt{3}}{3}\]
anonymous
  • anonymous
Thank you so much
jim_thompson5910
  • jim_thompson5910
no problem

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