SOLUTION: Given cos x=-1/3,find the value of k.(answer:3m sin x) https://app.box.com/s/o07hisesepyg2ck9n7pdqf4sxkfzserl

Algebra ->  Trigonometry-basics -> SOLUTION: Given cos x=-1/3,find the value of k.(answer:3m sin x) https://app.box.com/s/o07hisesepyg2ck9n7pdqf4sxkfzserl      Log On


   

Question 1002893: Given cos x=-1/3,find the value of k.(answer:3m sin x)
https://app.box.com/s/o07hisesepyg2ck9n7pdqf4sxkfzserl
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!

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you are given that cos(x) = -1/3.

that puts the angle in the second quadrant.

you are given that cos(x) = -1/3.

this means the ratio of the adjacent side to the hypotenuse is equal to -1/3.

the adjacent side is shown as m.

if you let h = the hypotenuse, you get the ratio m / h = -1 / 3.

cross multiply to get 3m = -h

solve for h to get h = -3m.

now the opposite side is shown as k.

sin(x) is therefore equal to k / -3m.

solve for k to get k = -3m * sin(x).

they show the answer as k = 3m * sin(x).

this, in my opinion, is in error.

it will only be true if they showed the adjacent side as -m rather than m.

in that case, the ratio would have been -m / h = -1 / 3.

cross multiply to get -3m = -h.

solve for h to get h = 3m.

sin(x) is then equal to k/3m and you get k = 3m * sin(x) as they have shown is the answer.

if, in fact, they showed the solution as k = -3m * sin(x), then the solution they showed is correct.

otherwise the error stands as i have indicated.

m should have been shown as -m.

that's my opinion.