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#