Calculate arcos(cos 2pi/3) + arcos(cos 5pi/3)

Question

help plz

Answer 1

arcos(cos 2pi/3) + arcos(cos 5pi/3)

= pi or 180 degrees or 3.14159

Answer 2

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

Answer 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

Answer 4

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

Answer 5

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

Answer 6

thank u all <3