# Question Video: Solving an Equation Using the Inverse Cosine Function Mathematics

Given that π₯ is an acute angle and 2β(2) cos (π₯) = 1 + β(3), determine the value of π₯ in radians.

01:52

### Video Transcript

Given that π₯ is an acute angle and two root two multiplied by cos π₯ is equal to one plus root three, determine the value of π₯ in radians.

In this question, weβre told that angle π₯ is an acute angle. Since the value of π₯ needs to be given in radians, we know that π₯ is greater than zero and less than π over two. We will calculate this value of π₯ by solving the equation two root two multiplied by cos π₯ is equal to one plus root three.

Our first step is to divide both sides by two root two. This means that cos π₯ is equal to one plus root three divided by two root two. Next, we will use our knowledge of the inverse trigonometric functions, where the inverse cos of cos π₯ equals π₯ when π₯ lies between zero and π radians. Taking the inverse cosine of both sides of our equation gives us π₯ is equal to the inverse cos of one plus root three divided by two root two. Ensuring that our calculator is in radian mode, we can type the right-hand side into the calculator. This gives us a value of π over 12 or one twelfth π.

The value of π₯ in radians that satisfies the equation two root two multiplied by cos π₯ is equal to one plus root three is π over 12.