If tan (x) = 3/4, what is cos (x)?

1 Answer
Mar 20, 2018

cosine (x) = 4 over 5
cos (x) = 4/5

Explanation:

First you must apply sohcahtoa
it means
sine = opposite side over hypotenuse
sine = opposite/hypotenuse
cosine = adjacent side over hypotenuse
cosine = adjacent/hypotenuse
tangent = opposite side over adjacent side
tangent = opposite/adjacent

then
solve the unknown by applying the Right Triangle Theorem.
draw a right triangle.
label the parts where
a is the opposite side
b is the adjacent side
c is the hypotenuse

Solve the unknown. The hypotenuse using
a^2 + b^2 = c^2
since the given tan x= 3/4
it means
tan = opposite/adjacent
a = opposite side = 3
b = adjacent side = 4
c = hypotenuse = ??
a^2 + b^2 = c^2
substitute the value
(3)^2 + (4)^2 = c^2
9 + 16 = c^2
25 = c^2
get the square root of 25
it is equal to 5
therefore
c = 5
c = hypotenuse = 5
cos = adjacent/hypotenuse
cos (x) = 4 over 5
cos (x) = 4/5