The problem: tan x = 5/12 and sec x = -13/12?

Answer 1

Yes it is true for x=200.62 degrees.

Carefuly schetch tan(x) and sec(x) [sec(x)=1/cos(x)] and you will see the answer or let your fingers do the calculator walk :).


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Answer 2

tan x = sin x / cos x

sec x = 1/ cos x

If sec x = -13/12, then cos x = -12/13

cos x is the adjacent over the hypotenuse while sin x is the opposite over the hypotenuse.

So, if cos x = -12/13, then sin x has to be -5/13. The '13's and the negative signs will cancel, leaving you with 5/12 for tan x.

That makes x approximately 202.6 degrees or approximately 3.58 radians. (You could have simply taken the arctan of 5/12, but that wouldn't tell you which quadrant you were in. You have be in the third quadrant to have both a negative sine and cosine.)

Answer 3

tan(A) = y/x
sec(A) = r/x

y = 5
r = -13
x = 12

cos(A) = x/r
sin(A) = y/r
csc(A) = r/y
cot(A) = x/y

cos(x) = -12/13
sin(x) = -5/13
csc(x) = -13/5
cot(x) = 12/5

Answer 4

may want to be a little more specific in what you are looking for