cos (2x) = cos x
2 cos^2 x -1 = cos x using the double angle formula
2 cos ^2 x -cos x -1 =0
factor
(2 cos x+1) ( cos x -1) = 0
using the zero product property
2 cos x+1 =0 cos x -1 =0
2 cos x = -1 cos x =1
cos x = -1/2 cos x=1
taking the arccos of each side
arccos cos x = arccos (-1/2) arccos cos x = arccos 1
x = 120 degrees x=-120 degrees x=0
remember you get 2 values ( 2nd and 3rd quadrant)
these are the principal values
now we need to add 360
x = 120+ 360n x=-120+ 360n x = 0 + 360n where n is an integer
Answer:
12,8
Step-by-step explanation:
Just line them up and you will arrive at your answer:
5,8
+ 7
_____
12,8
I am joyous to assist you anytime.
Answer: -20/3
Step-by-step explanation:
I’m not great at math so I could easily be wrong, but
I divided the 18.24 millimeters by 12 pennies and got 1.52
So if the pennies are all the same size, each penny should 1.52 millimeters.
To show work:
18.24/12=1.52
a is the answer, as i is irrational no
