## keelyjm 2 years ago help with inverse trig functions?

1. keelyjm

Find the exact value of sin(arctan(2)). For full credit, explain your reasoning.

2. AravindG

well first try to make than tan inverse inside the bracket to sin inverse so that we get sin (sin-1)

3. AravindG

drawing a triangle can help you do that

4. keelyjm

Drawing a triangle will help change tan-1 to sin-1?

5. hartnn

Let arctan 2 = x so, tan x = 2 /1 since you know tan x = opposite side/adjacent side make a right angled triangle with one leg =2 and other leg = 1 |dw:1359734613467:dw| now can you find the hypotenuse ??

6. AravindG

yep :) just draw ..you will see

7. hartnn

once you find the hypotenuse, find sin x.

8. keelyjm

sqrt 5

9. hartnn

because sin(arctan(2)). = sin x

10. hartnn

yes, so sin x = sin (arctan 2) =...?

11. keelyjm

sqrt5?

12. hartnn

thats the hypotenuse . sin ratio = opposite side / hypotenuse =... ?

13. keelyjm

oh so it's 2/sqrt5

14. hartnn

yup .

15. hartnn

any doubts ?

16. keelyjm

alright and what about finding the exact real value of arccos(sqrt2/2)?

17. keelyjm

no I understand that now that you have to use a tiangle to solve it

18. hartnn

arccos(sqrt2/2) =x cos x = sqrt2/2 = 1/sqrt 2 for what value of angle 'x' is cos x = 1/sqrt 2 its one of the standard angle....

19. hartnn

also, next time please ask new question in new post...

20. keelyjm

okay sorry. I am not sure how you got cos x = sqrt2/2 = 1/sqrt 2 ?

21. hartnn

you know unit circle ? which defines standard values of sin/cos for standard angles...

22. hartnn

i suggest you learn and remember all standard angles and values..

23. keelyjm

yes i know the unit circle. is that pi/4? 45 degrees?

24. hartnn

yes, exactly :)

25. keelyjm

so pi/4 would be the exact real value?

26. satellite73

$\arccos(\frac{\sqrt{2}}{2})$ see if you recall an angle whose cosine is $$\frac{\sqrt{2}}{2}$$

27. hartnn

yes. pi/4 in radians 45 in degrees.

28. keelyjm

Thank you so much!

29. hartnn

welcome ^_^