## anonymous one year ago y = 2tan(theta) . Find the value of tangent, then double it. It's a table with pi/6 through 2pi

1. jim_thompson5910

Can you post a screenshot of the full problem?

2. anonymous

yeah, just one moment

3. anonymous

sorry my computer is super slow

4. anonymous

5. jim_thompson5910

that's fine

6. jim_thompson5910

ah, I see now

7. jim_thompson5910

so what you do is replace $$\Large \theta$$ (greek letter theta) with the numbers in the top row Use the unit circle or a table to find that $\Large \tan(\theta) = \tan(0) = 0$ $\Large \tan(\theta) = \tan\left(\frac{\pi}{6}\right) = \frac{\sqrt{3}}{3}$ $\Large \tan(\theta) = \tan\left(\frac{\pi}{4}\right) = 1$ etc etc

8. jim_thompson5910

then you double each result $\Large 2*\tan(\theta) = \tan(0) = 2*0 = 0$ $\Large 2*\tan(\theta) = 2*\tan\left(\frac{\pi}{6}\right) = 2*\frac{\sqrt{3}}{3} = \frac{2\sqrt{3}}{3}$ $\Large 2*\tan(\theta) = 2*\tan\left(\frac{\pi}{4}\right) = 2*1 = 2$ etc etc

9. anonymous

so it's just the coordinate points ?

10. jim_thompson5910

yeah the y coordinates of each point on the graph of y = tan(x)

11. jim_thompson5910

2*tan(x) I mean

12. anonymous

ugh thank you, you're a life saver

13. jim_thompson5910

you're welcome

14. anonymous

wait how'd you get $\pi/4$ to be 1

15. jim_thompson5910

tan of pi/4 is 1

16. jim_thompson5910

if you look at the unit circle, you'll find that sine and cosine have the same value at pi/4 sin(pi/4) = cos(pi/4)

17. jim_thompson5910

because of that and because tangent = sine/cosine, the two equal values divide to 1

18. anonymous

oooooooh okay, i get it now

19. jim_thompson5910

I'm glad it's making more sense

20. anonymous

Yeah I'm the worst at trigonometry lol

21. jim_thompson5910

I'm sure with more practice, you'll get better at it

22. anonymous

this is my third year learning this and I still haven't learned it :/

23. jim_thompson5910

then a different approach is needed

24. anonymous

yes, badly so for pi/3 , would it be radical 3 ? or do the 2's not cancel out ?

25. jim_thompson5910

the 2s will cancel leaving sqrt(3), correct

26. anonymous

Okay, I just wanted to make sure cause I've seen it where the 2's aren't being canceled out

27. anonymous

and since I'm doubling it, would it be $2\sqrt{3}$ or ?

28. jim_thompson5910

I'd have to see the problem (where you didn't see the 2s cancel), but you should have this $\Large \tan\left(\theta\right) = \frac{\sin\left(\theta\right)}{\cos\left(\theta\right)}$ $\Large \tan\left(\frac{\pi}{3}\right) = \frac{\sin\left(\frac{\pi}{3}\right)}{\cos\left(\frac{\pi}{3}\right)}$ $\Large \tan\left(\frac{\pi}{3}\right) = \frac{\sqrt{3}/2}{1/2}$ $\Large \tan\left(\frac{\pi}{3}\right) = \frac{\sqrt{3}}{2}\times\frac{2}{1}$ $\Large \tan\left(\frac{\pi}{3}\right) = \frac{\sqrt{3}}{\cancel{2}}\times\frac{\cancel{2}}{1}$ $\Large \tan\left(\frac{\pi}{3}\right) = \sqrt{3}$

29. jim_thompson5910

yes, $\Large 2\tan\left(\frac{\pi}{3}\right) = 2\sqrt{3}$

30. anonymous

Okay, I think I'm getting a little more. I saw it on some website and it was a table like I'm filling out and the 2's weren't canceled out

31. jim_thompson5910

hmm, strange

32. anonymous

but it just makes sense to cancel them out to me so I figured whoever made that table just forgot that step maybe?

33. jim_thompson5910

that's possible

34. jim_thompson5910

even teachers who write the problems and examples make typos

35. anonymous

I know many lol. But anyways, thank you so much

36. jim_thompson5910

sure thing