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## Find the value of ALL the other five trigonometric functions, given tanx= 4/11, secx<0.

Thanks for the help! If you could please show all your work? Thanks again!

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# 3 Answers

Kirill and Felice gave good answers, but I wanted to add this to eliminate any confusion.

We can only use trig functions with right triangles, so you have to use Pythagorean's Theorem to solve for the hypotenuse: a2+b2=c2. a and b = 4 and 11, in either order, according to the problem. Therefore, c2=137; c=sqrt137.

I hope that fills in any gaps. Kirill and Felice covered the rest of the explanation.
Since sec(x)<0 and tan(x)>0, angle is in the third quadrant.

cot(x)=11/4
cos(x)=-√[1/(1+tan2(x))]=-√[1/(1+16/121)]=-11/√137;
sin(x)=-√[1-cos2(x)]=-√[1-121/137]=-4/√137
sec(x)=-(√137)/11
cosec(x)=-(√137)/4
Well if we use the trigonometric functions

sin X = opposite / hypotenuse
cos X = adjacent / hypotenuse
tan X = opposite/ adjacent
csc X = hypotenuse / opposite
sec X = hypotenuse/adjacent
ctn X = adjacent/opposite

We know that the hypotenuse = sqrt(adjacent+ opposite2)
from your given tan X = 4/11 we could say the the opposite was 4 and adjacent was 11

so our hypotenuse would be sqrt(112 + 42) = sqrt (121+16) = sqrt(137) = 11.7

so your sin X = opp/hyp = 4/11.7

fill in the rest for the other 4 functions