Question

Find the exact value of cos-1the quantity square root of two divided by two.

Answer 1

if I understand the assignment correctly, this is the equation you are looking for:

\[x = \cos ^{-1}\frac{ \sqrt{2} }{ 2 }\]

draw yourself a radiant circle:

as you can see, you equation has two solutions. now you just have to add +2*k*pi to each of the solutions because solutions can be shifted by a full circle and still have the same value.
can you write down the final solutions now? if you need more help, feel free to ask

Answer 2

thats the equation

Answer 3

How did you know where the points on the unit circle are?

Answer 4

cos^-1 (sqrt(2)/2) is equal to pi/4.
that is something you can check with your calculator, but it is good (maybe even mandatory) to know the values of sin and cos of the important points on radian circle.
this is a good reference:

http://www.geocities.ws/petrinamaher/UnitCircle.GIF

you read the values of sinus on the y-axis, and that would be the second number in every bracket on this picture.
you read the values of cosinus on the x-axis, and that would be the first number in every bracket.

we you found that sqrt(2)/2 is pi/4, you will see that the same value has 7pi/4

ask if something is unclear;)

Answer 5

Thanks wall