Question

If possible, find the exact value of
sec[arctan(-5)]. Pls explain steps to solve such questions....

Answer 1

http://answers.yahoo.com/question/index?qid=20110717174125AAoMvGn
http://www.wolframalpha.com/input/?t=crmtb01&f=ob&i=sec(arctan(-5))

between these 2 links, you can find methodology and the answer

Answer 2

1) draw your triangle on the unit circle. It has to be in the 2nd quadrant, because that's where the tangent is defined to be negative. See the figure
2) If the arctan of (-5) is the angle that gives you -5 when you take the tangent of it.
So the ratio of the opposite to the adjacent. The Hypoteneuse can then be done by Sqrt(5^2 +1^2) = sqrt(26).

3) the secant is 1/cosine or the ration of the Hypoteneus to the adjacent of sqrt(26}/-1
4) therefore the secant of the arctan of -5 should be -sqrt(26)

Answer 3

it should say ratio of the Hyp. To the Adj. ,,, OR sort(26)/(-1)

Answer 4

@freewilly922
In your answer you say that "1) draw your triangle on the unit circle. It has to be in the 2nd quadrant, because that's where the tangent is defined to be negative.
But tan is positive only in the Ist and IIIrd quadrants. It is negative in 2nd and 4 th quadrants so why don,t we use 4th quadrant??

Answer 5

I see what you are saying, and the result would be positive sqrt(26) since the secant is only the x values. I have to think about this, does this mean there are two answers? plus and minus sort(26)?

Answer 6

??????That is what I want to know....☺

Answer 7

Since tan x would not be a function if inverted, only one cycle of tan x is used when doing arctan. They choose the cycle that includes (0,0) so domain x goes from -π/2 to π/2 (non-inclusive) and range tan x goes from -∞ to ∞

So the inverse, those switch and domain is now all numbers while range is -π/2 < arctan x < π/2

so thats why. go figure. So the answer should be +sqrt(26) then and we should have only used quadrant 1 or 4 not 2.

Answer 8

Stole this off some web site.

Answer 9

But you did make the effort for explaining me.....☺
Thanks for your help and medal for you...