## 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.

1. jim_thompson5910

Hint: Pythagorean Trig Identity $\Large \sin^2(x) + \cos^2(x) = 1$

2. anonymous

Ok, so how would I continue off that? May you guide me through the problem please?

3. 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 $\Large \sin^2(x) + \cos^2(x) = 1$ $\Large \frac{1}{4} + \cos^2(x) = 1$

4. jim_thompson5910

now isolate cos(x)

5. anonymous

we subract 1/4 from both sides

6. anonymous

so now we square root both sides right?

7. jim_thompson5910

correct on both statements

8. anonymous

then how do we get tangent

9. jim_thompson5910

$\Large \tan(x) = \frac{\sin(x)}{\cos(x)}$

10. anonymous

Ok, hold on. Let me put everything together.

11. anonymous

cos(x) = $\sqrt{.75}$ is that how it should be written

12. jim_thompson5910

or $\Large \sqrt{\frac{3}{4}} = \frac{\sqrt{3}}{\sqrt{4}} = \frac{\sqrt{3}}{2}$

13. jim_thompson5910

most books I've seen use $\Large \frac{\sqrt{3}}{2}$

14. anonymous

oh ok, so $\tan(x) = \frac{ 1 }{ 2 } /\frac{ \sqrt{3} }{ 2 }$

15. jim_thompson5910

Yes correct. Now simplify

16. anonymous

How would I do that?

17. jim_thompson5910

|dw:1439850551781:dw|

18. jim_thompson5910

|dw:1439850577166:dw|

19. anonymous

so the answer is $\frac{ 1 }{ \sqrt{3} }$

20. jim_thompson5910

rationalizing the denominator makes that turn into $\Large \frac{\sqrt{3}}{3}$

21. anonymous

Thank you so much

22. jim_thompson5910

no problem