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anonymous
 one year ago
If sine of x equals 1 over 2, what is cos(x) and tan(x)? Explain your steps in complete sentences.
anonymous
 one year ago
If sine of x equals 1 over 2, what is cos(x) and tan(x)? Explain your steps in complete sentences.

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jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1Hint: Pythagorean Trig Identity \[\Large \sin^2(x) + \cos^2(x) = 1\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Ok, so how would I continue off that? May you guide me through the problem please?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1since sine is 1/2, squaring that gives you 1/4 you can replace all of sin^2 with 1/4 like this \[\Large \sin^2(x) + \cos^2(x) = 1\] \[\Large \frac{1}{4} + \cos^2(x) = 1\]

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1now isolate cos(x)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0we subract 1/4 from both sides

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so now we square root both sides right?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1correct on both statements

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0then how do we get tangent

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1\[\Large \tan(x) = \frac{\sin(x)}{\cos(x)}\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Ok, hold on. Let me put everything together.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0cos(x) = \[\sqrt{.75}\] is that how it should be written

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1or \[\Large \sqrt{\frac{3}{4}} = \frac{\sqrt{3}}{\sqrt{4}} = \frac{\sqrt{3}}{2}\]

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1most books I've seen use \[\Large \frac{\sqrt{3}}{2}\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0oh ok, so \[\tan(x) = \frac{ 1 }{ 2 } /\frac{ \sqrt{3} }{ 2 }\]

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1Yes correct. Now simplify

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0How would I do that?

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1dw:1439850551781:dw

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1dw:1439850577166:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so the answer is \[\frac{ 1 }{ \sqrt{3} }\]

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1rationalizing the denominator makes that turn into \[\Large \frac{\sqrt{3}}{3}\]
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