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!

Question

amistre64 · Answer

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

amistre64 · Answer

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

amistre64 · Answer

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

amistre64 · Answer

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

amistre64 · Answer

attachment

amistre64 · Answer

the answer is 5 according to the drawing

anonymous · Answer

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

amistre64 · Answer

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

amistre64 · Answer

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

amistre64 · Answer

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

anonymous · Answer

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

amistre64 · Answer

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

anonymous · Answer

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

amistre64 · Answer

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

amistre64 · Answer

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

amistre64 · Answer

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

anonymous · Answer

what is base?

anonymous · Answer

okay i got it, thanks!

amistre64 · Answer

:)  youre welcome  :)

anonymous · Answer

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