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

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

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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, we’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œ‹ 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œ‹ 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œ‹ over 12 or one twelfth πœ‹.

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œ‹ over 12.

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