SOLUTION: How to get the exact value of tan(sin^(-1) 1/3)?? Please!

Algebra ->  Test -> SOLUTION: How to get the exact value of tan(sin^(-1) 1/3)?? Please!      Log On


   

Question 433277: How to get the exact value of tan(sin^(-1) 1/3)?? Please!
Found 2 solutions by Alan3354, katealdridge:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Angle A = arcsin(1/3)
sin(A) = 1/3
cos%28A%29+=+sqrt%281+-+%281%2F3%29%5E2%29+=+sqrt%288%2F9%29
tan%28A%29+=+sin%28A%29%2Fcos%28A%29+=+%281%2F3%29+%2F+%28sqrt%288%29%2F3%29
tan%28A%29+=+%281%2F3%29%2A%283%2Fsqrt%288%29%29+=+1%2Fsqrt%288%29+=+sqrt%282%29%2F4
------------
Use a calculator to check.
arcsin(1/3) =~ 19.47 degs
tan(19.47) = 0.3535533
sqrt(2)/4 = 0.3535533

Answer by katealdridge(100) About Me  (Show Source):
You can put this solution on YOUR website!
sin%5E%28-1%29%281%2F3%29 means that there is a right triangle with the vertical side = 1 and the hypotenuse = 3, because sin%28theta%29=opposite%2Fhypotenuse
Using the Pythagorean Theorem, you can find the value of the adjacent side.
x%5E2%2B1%5E2=3%5E2
x=2sqrt%282%29
Since tan%28theta%29=opposite%2Fadjacent then
tan%28theta%29=1%2F%282sqrt%282%29%29=sqrt%282%29%2F4