Question

How do I evaluate arccsc(sec2)?

Answer 1

isn't it sec(2)?

Answer 2

oh did i misunderstand the problem?
its not sec^2

Answer 3

cause the question is arcsc(sec(2))

Answer 4

\[\csc ^-1(\sec (2))\]

Answer 5

oh in this case use a calculator

http://www.wolframalpha.com/input/?i=arccsc%28sec%282%29%29

Answer 6

how do you do it by hand?

Answer 7

the solution is suppose to be pi/2 - 2, but i dont know how to get it.

Answer 8

\[\theta = \csc ^{-1} (\sec 2)\]
\[\csc \theta = \sec 2\]
take reciprocal
\[\sin \theta = \cos 2\]
draw triangle

from triangle
\[\tan (\frac{\pi}{2} - 2) = \frac{\sin \theta}{\cos \theta} = \tan \theta\]
therefore
\[\theta = \frac{\pi}{2} - 2\]

Answer 9

did that make sense?

Answer 10

i'm kind of confused on how you drawn the triangle.

Answer 11

ahh ok

cos(2) = adj/hyp = sin(theta)/1

this is why hypotenuse is 1 and adjacent side is sin(theta)
remember in right triangle the 2 angles must add up to 90 or pi/2 so if one angle is 2 the other must be (pi/2) -2

Answer 12

Ok, I think I got it now. Thanks!

Answer 13

:)

Answer 14

I might need your help again later :)