If sin x = -12/13 and tan x is positive, find the values of cos x and tan x.
since sinx = -12/13, and tanx is positive, x must be in quad III
in your triangle:
sinx = -12/13 ----> the given
cosx = -5/13
tanx = -12/-5 = 2.4
To find the values of cos x and tan x, we'll use the following trigonometric identities:
1. sin^2(x) + cos^2(x) = 1
2. tan(x) = sin(x) / cos(x)
Given that sin x = -12/13, we can find cos x using the first identity:
sin^2(x) + cos^2(x) = 1
(-12/13)^2 + cos^2(x) = 1
144/169 + cos^2(x) = 1
cos^2(x) = 1 - 144/169
cos^2(x) = 169/169 - 144/169
cos^2(x) = 25/169
cos x = ±√(25/169)
Since we know that cos x is positive (which was not explicitly mentioned but is assumed because tan x is positive), we take the positive square root:
cos x = √(25/169)
cos x = 5/13
Now, to find tan x, we'll use the second identity:
tan(x) = sin(x) / cos(x)
tan(x) = (-12/13) / (5/13)
tan(x) = (-12/13) * (13/5)
tan(x) = -12/5
Therefore, the values of cos x and tan x are cos x = 5/13 and tan x = -12/5.