Question

Cos x= 3/4, s in quadrant 1

Answer 1

Answer: x = 41.4°

Step-by-step explanation:

We want to solve:

Cos(x) = 3/4

Such that this is on quadrant 1.

(if x is in degrees, the possible values of x will be: 0° ≤ x ≤ 90°)

To solve this we need to remember the inverse functions.

If we have two functions f(x) and g(x), these functions are inverses if:

f( g(x) ) = x

g( f(x) ) = x

Then the inverse of the cosine function (this function is "arcos(x)") is such that:

Arcos( cos(x) ) = x

Then in our equation:

Cos(x) = 3/4

We can apply the inverse function to both sides to get:

Arcos(Cos(x)) = Arcos(3/4)

x = Arcos(3/4)

(To find the Arcos function in your calculator, you need to use the button "inv" and then the "cos" button, and remember to have your calculator in deg mode)

x = Arcos(3/4) = 41.4°