tan is the ratio of the opposite side to the adjacent side. so in this, tan x = -12/5 it means that in a right triangle, 2 of its sides are 12 and 5. so solving for the 3rd side
c^2 = a^2 + b^2
c^2 = 144 + 25
c^2 = 169
c = 13 so the hypotenuse is 13
cos is the ratio of the adjacent side to the hypotenuse. since it was given before that the adjacent side is 5, then
the ratio of adjacent to hypotenus is 5/13
but it is also stsated that x is between 90 and -90, so i suppose it is Quadrant 4. it is defined that the only positive functions in Q4 are cosine and secant
there fore cos is negative.
thus cosX = 5/13. i dont know why your answer is negative, but i believe thati'm right. butplease confirm whether or not i really am righjt
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build the triangle...
if tan x is negative, and x is between (- 90º, 90º), then cos x must be positive !
x is in the fourth quadrant...
side opposite x = - 12
side adjacent to x = 5
hypotenuse = 13
cos x = 5/13
euclid
tan is the ratio of the opposite side to the adjacent side. so in this, tan x = -12/5 it means that in a right triangle, 2 of its sides are 12 and 5. so solving for the 3rd side
c^2 = a^2 + b^2
c^2 = 144 + 25
c^2 = 169
c = 13 so the hypotenuse is 13
cos is the ratio of the adjacent side to the hypotenuse. since it was given before that the adjacent side is 5, then
the ratio of adjacent to hypotenus is 5/13
but it is also stsated that x is between 90 and -90, so i suppose it is Quadrant 4. it is defined that the only positive functions in Q4 are cosine and secant
there fore cos is negative.
thus cosX = 5/13. i dont know why your answer is negative, but i believe thati'm right. butplease confirm whether or not i really am righjt
hope this helps :))
tan X = - 12/5
=> tan² X = (- 12/5)² = 144/25
=> 1 + tan² X = sec² X = 1 + (144/25) = 169/25
=> sec X = ± 13/5
=> cos X = ± 5/13
When X lies between - 90º and + 90º, cos X is positive
Hence rejecting the -ve value, we have cos X = + 5/13
1 + tan^2 x = 1/cos^2 x ---> 1+ ( -12/5)^2 = 1/cos^2 x
cos^2 x = 25/169 ---> cos x = 5/13