Video Transcript
Given that 𝑥 is an acute angle and two root two multiplied by cos 𝑥 is equal to one plus root three, determine the value of 𝑥 in radians.
In this question, we’re told that angle 𝑥 is an acute angle. Since the value of 𝑥 needs to be given in radians, we know that 𝑥 is greater than zero and less than 𝜋 over two. We will calculate this value of 𝑥 by solving the equation two root two multiplied by cos 𝑥 is equal to one plus root three.
Our first step is to divide both sides by two root two. This means that cos 𝑥 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 𝑥 equals 𝑥 when 𝑥 lies between zero and 𝜋 radians. Taking the inverse cosine of both sides of our equation gives us 𝑥 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 𝑥 in radians that satisfies the equation two root two multiplied by cos 𝑥 is equal to one plus root three is 𝜋 over 12.
