Find cos x if tan x = negative 2 square root of 2 divided by 2 and sin x “ square root 6 divided by 3

Answer 1

In Precalc, you learn tan(x) = sin(x)/cos(x). This means if you know two of the three you can find the third.

So:

tan(x) = -2sqrt(2)/2 = -sqrt(2),

and

sin(x) = sqrt(6)/3

Do a little algebra to get cos(x) = sin(x)/tan(x). Then cos(x) = [sqrt(6)/3]/[-sqrt(2)]

Now the two square roots can be combined together from the rule: sqrt(x)/sqrt(y) = sqrt(x/y).

So cos(x) = -sqrt(6/2)/3 = -sqrt(3)/3

(This is when you realize Wyzant really needs a math equation editor function.)

Robert Clark

Answer 2

Set up using a right triangle using information given for the tan(x). ( Opposite/adjacent). Use the pythagorean theorem to find the hypotenuse. Then cosine=a/h, however sin(x) is positive. So cos(x)=-(a/h), since tan(x)=sin(x)/cos(x) and tan is negative.