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:
c
Step-by-step explanation:
Since it is a ratio to those who get bonus and don't, it is 24:80.
you must add 24+56 to get total amount of employees.
24+56=80
therefore, the answer is 24:80
4(m + 2) expanded is 4 x m and 4 x 2
simplified: 4m + 8
Answer:
i think it would be a model.
Step-by-step explanation:
The interquartile range is 12-6=6
