evaluate cos(inverse)1/2

Question

evaluate cos(inverse)1/2
Evaluate arccos1/2.

I don't understand this? What does it mean to evaluate? How do I do this? What are the steps? Please show step by step with explanation. I don't know how to do this. Also, how do I put the answer? There are no answer choices, just a box to type the answer. I really dont understand.

I am asking this question again because I still do not understand. I can only have one answer...? 

 

Answer 1

"Evaluate" means "find the value of".

 

For example, if you were asked to evaluate 3x + 4 when x is 3, you would put 3 in for x and do the calculation, which would get you 13.

 

By this point, you should have started to be taught about the inverse trigonometric functions, such as arccos (also known as cos^-1).  Instead of finding the cosine of a number, they want you to find the number whose cosine is 1/2.

 

If you look at the graph of the cosine function, you see that there are many numbers that have a cosine of 1/2.  It repeats over and over.  So in order to make arccos a function, with only one value, the definition is restricted so that the range is from 0 to π.

 

When you were studying the trigonometric functions recently, you probably saw a chart that showed the sin, cos and tan values for the most important angles.  There you would have seen that cos π/3 = 1/2.  So  π/3 is one of the angles whose cos is 1/2.  And since π/3 is in the interval from 0 to π, that satisfies the requirement.