Calculate arcos(cos 2pi/3) + arcos(cos 5pi/3)
help plz
arcos(cos 2pi/3) + arcos(cos 5pi/3)
= pi or 180 degrees or 3.14159
Isn't arccos(cos x) = x ?? (they are inverse operators)
e.g. arccos(cos 60°) = arccos( 1/2 ) = 60°
then
arccos(cos 2pi/3) + arccos(cos 5pi/3)
= 2π/3 + 5π/3
= 7π/3
I disagree, it should be π and I can say that will 100% certainty.
arccos(cos (2π/3)) + arccos(cos (5π/3)) = π
arccos is the cos-1() button on your calculator so change your calc to rads and type that in, you will get π
If your question means:
arcos ( cos ( 2 π / 3 ) ) + arcos ( cos ( 5π / 3 ) )
then
arcos ( cos ( 2 π / 3 ) ) = 2 π / 3
cos ( 5 π / 3 ) = cos ( 6 π / 3 - π / 3 ) = cos ( 2 π - π / 3 )
Since:
cos ( 2 π - θ ) = cos θ
cos ( 5 π / 3 ) = cos ( 2 π - π / 3 ) = cos ( π / 3 )
arcos ( cos ( 5 π / 3 ) ) = arcos ( cos ( π / 3 ) ) = π / 3
arcos ( cos ( 2 π / 3 ) ) + arcos ( cos ( 5π / 3 ) ) =
2 π / 3 + π / 3 = 3 π / 3 = π
You are right, should have caught that
(btw, I am well aware which buttons are what.)
By convention, the range of arccos is limited to 0 to +π
so cos 2π/3 = -1/2
arccos( -1/2) = 2π/3
cos (5π/3) = 1/2
arccos (1/2) = π/3
thus
arccos(cos 2pi/3) + arccos(cos 5pi/3)
= 2π/3 + π/3 = 3π/3 = π
thank u all <3
To solve this problem, we'll start by understanding the concept of arccosine and its properties. The arccosine function, denoted as arcos(x) or acos(x), is the inverse function of cosine. It returns the angle whose cosine is the given value.
In this case, we want to find the sum of arccos(cos(2π/3)) and arccos(cos(5π/3)).
First, let's determine the values of cos(2π/3) and cos(5π/3):
cos(2π/3) = -1/2
cos(5π/3) = 1/2
Now, substituting these values into the arccosine function:
arcos(-1/2) + arcos(1/2)
To calculate arcos(-1/2), we need to find the angle whose cosine is -1/2. This angle is 2π/3.
Similarly, to calculate arcos(1/2), we need to find the angle whose cosine is 1/2. This angle is π/3.
So, the final expression becomes:
2π/3 + π/3
Now we can simplify the expression:
2π/3 + π/3 = 3π/3 = π
Therefore, the sum arcos(cos(2π/3)) + arcos(cos(5π/3)) is equal to π.