Video Transcript
Find the value of 𝑋 in degrees given cos of 𝑋 equals one-half, where 𝑋 is an acute angle.
Since 𝑋 is an acute angle, we know it must be greater than zero degrees and less than 90 degrees. And we need to find all the solutions in this range such that cos 𝑋 is equal to one-half. By sketching the graph of 𝑦 equals cos 𝑋 between zero and 90 degrees, we see that the line 𝑦 is equal to one-half intersects our curve once in the given range. This means that there will be one solution to the equation between zero and 90 degrees. Recalling our knowledge of the special angles, we know that cos of 60 degrees is equal to one-half. This means that 𝑋 is equal to 60 degrees.
An alternative method to solve the equation would be to take the inverse cosine of both sides such that 𝑋 is equal to the inverse cos of one-half. Typing the right-hand side into our calculator, we obtain the solution 𝑋 is equal to 60 degrees. And since 𝑋 is an acute angle, this is the only solution.
