SOLUTION: Please help me answer this question regarding sec, and finding csc ϴ. Problem with possible results https://s30.postimg.org/prisl7n01/sec_csc.png Thank you.

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Question 1063068: Please help me answer this question regarding sec, and finding csc ϴ.
Problem with possible results

https://s30.postimg.org/prisl7n01/sec_csc.png
Thank you.
Found 3 solutions by Apples_21, rothauserc, ikleyn:
Answer by Apples_21(13) About Me  (Show Source):
Answer by rothauserc(4718) About Me  (Show Source):
You can put this solution on YOUR website!
sec(pi/2 - theta) = sqrt(3)/2 then
:
Note that sec(pi/2 - theta) = csc(theta)
:
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therefore the answer is C)
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:
How do we prove this?
:
Note that cos(pi/2) = 0 and sin(pi/2) = 1
:
sec(pi/2 - theta) = 1 / cos(pi/2 - theta) = 1 / (cos(pi/2)cos(theta) + sin(pi/2)sin(theta)) = 1 / sin(theta)
:
1 / sin(theta) = csc(theta)
:

Answer by ikleyn(52835) About Me  (Show Source):
You can put this solution on YOUR website!
.
Dear tutor "rothauserc" !

sec is always greater or equal to 1, OR lesser or equal to -1.

It CAN NOT be between -1 and 1.

The number sqrt%283%29%2F2 = 0.866 is between -1 and 1.

IT CAN NOT BE the value of "sec" ! ! ! ! ! ! ! ! ! !


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