Question

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

Answer 1

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`