## anonymous one year ago Find the exact value of tan inverse

1. anonymous

2. UnkleRhaukus

tan theta = opp / adj

3. UnkleRhaukus

(there is no inverse)

4. anonymous

this is a dumb question.. but what does the theta sign look like?

5. UnkleRhaukus

theta : $$\theta$$

6. anonymous

that's the sign I used but I thought it meant inverse :0

7. UnkleRhaukus

$\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$$\Downarrow$$\theta = \tan^{-1}\left(\frac{\text{opposite}}{\text{adjacent}}\right)=\arctan\left(\frac{\text{opposite}}{\text{adjacent}}\right)$

8. UnkleRhaukus

the question is only asking you to find $$\tan\theta$$, you don't have to compute the value of theta,

9. anonymous

It's saying the equation has too many equal signs

10. UnkleRhaukus

what is the length of the side opposite to theta in the diagram?

11. anonymous

is 6 the opp and 2 and 5 the adj?

12. UnkleRhaukus

yes, opp = 6 and adj = 2√5

13. anonymous

my calculator said it was 1/2 as the answer, but it said that 1/2 is not correct

14. UnkleRhaukus

$$\tan\theta = \dfrac{6}{2\sqrt 5}$$

15. UnkleRhaukus

now cancel the common factor

16. anonymous

what's the common factor?

17. UnkleRhaukus

$\tan\theta = \dfrac{6}{2\sqrt 5}=\dfrac{2\times3}{2\times\sqrt 5}=$

18. anonymous

$\tan \emptyset \frac{ 6}{ 5 }=\frac{ 3 }{ 5 }$

19. UnkleRhaukus

now rationalize the denominator $\tan\theta = \frac{6}{2\sqrt 5}=\frac{3}{\sqrt 5}=\frac{3}{\sqrt 5}\times\frac{\sqrt5}{\sqrt5}=$

20. anonymous

20..?

21. UnkleRhaukus

$\frac{3}{\sqrt 5}\times\frac{\sqrt5}{\sqrt5}=\frac{3\times\sqrt5}{\sqrt5\times\sqrt5}$ now simplify the denominator

22. anonymous

would it be 1 because 5 can go into 5 once?

23. UnkleRhaukus

$\sqrt5\sqrt5=\sqrt5^2= .....$

24. anonymous

i'm not even sure how to go about that :o

25. UnkleRhaukus

$√x^2 = x$

26. anonymous

oh gosh

27. UnkleRhaukus

ikr

28. anonymous

29. anonymous

my options don't even make sense then

30. UnkleRhaukus

we are very close to one of those

31. UnkleRhaukus

what is the square root of five squared?

32. anonymous

5? I think

33. anonymous

oh wait i did that wrong

34. UnkleRhaukus

yes, so what is our final answer?

35. anonymous

5 squared over

36. anonymous

3 I wanna say