How can I find the exact value of: sec[arctan(2)]

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How can I find the exact value of: sec[arctan(2)]

Mathematics
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|dw:1433030295384:dw|
let theta = arctan(2) this means that tan(theta) = 2 = 2/1 recall that tangent deals with opposite/adjacent, so because tan(theta) = 2/1, we know |dw:1433030381643:dw|
are you able to find the length of the hypotenuse?

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Other answers:

yes
the question is direct at @Tracy96
@jim_thompson5910 yep! I got it! So I gotta use Pythagorus, correct?
length^2+width^2=hypotenuse^ 2
correct @Tracy96
you have to use a^2 + b^2 = c^2 a = 1 b = 2 c = unknown for now |dw:1433030530767:dw|
@henryli is correct too!!
corect
@jim_thompson5910 right, so hypotenuse would be sqrt(5) ?
yep
yes that is correct |dw:1433030615675:dw|
now because I let theta = arctan(2), this means sec[arctan(2)] turns into sec(theta)
use the drawing to compute sec(theta)
@jim_thompson5910 Mhmm, and sec is just 1/cos right?
correct
correct
you can also think of secant as hypotenuse/adjacent
yeah
@jim_thompson5910 Thanks so much!! I really appreciate it!!
sounds like you got the final answer, yw

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