anonymous 5 years ago I doubt anyone knows, but I need to know step by step how to solve the trig equation: Secant [Sine-1 radical2/5] ....please help!

1. amistre64

the secant of sine inverse (sqrt(2)/5) is the question right? $$sec(sin(sqrt{2}/5)$$

2. amistre64

well: $$sin^{-1}(\sqrt{2}/5)$$

3. amistre64

you should be aware that the sin^-1 takes a number and gives back an angle between 0 and pi

4. amistre64

but easiest thing to do is make a triangle and draw a pic

5. amistre64

6. amistre64

the answer is 5 according to the drawing

7. anonymous

my book says 5 radical 23 over 23.... i solve for my triangle taking sine(x)= radical 2 over 5 and find the third side. But from here, i dont know how to find secant

8. amistre64

secant = hyp/adj ; its just the inverse of cosine

9. amistre64

it is this right? $sec(sin^{-1}(\frac{\sqrt{2}}{5})$

10. amistre64

i did sqrt(2)^2 = 4 lol ....

11. anonymous

yes, i just dont understand how the answer is 5 radical 23 over 23

12. amistre64

sqrt(25 - 2) = sqrt(23) for the bottom part then right?

13. anonymous

yeah i dont understand how to get to that part. i just got my triangle and then i dont know where to go from there using secant

14. amistre64

if you know 2 sides of a right triangle you can find the thirs by the pythagoreum thrm

15. amistre64

(sqrt(2))^2 + base^2 = (5)^2 2 + base^2 = 25 base^2 = 25-2 base^2 = 23 base = sqrt(23)

16. amistre64

secant(A) = hyp/base sec = 5/sqrt(23)

17. anonymous

what is base?

18. anonymous

okay i got it, thanks!

19. amistre64

:) youre welcome :)

20. anonymous

I've posted another tricky one if you can solve it for me, that'd be greatly appreciated!