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:
x = 8 tickets
Step-by-step explanation:
Given that,
Mage has $36 to spend on movie tickets.
Each movie ticket costs $4.50.
Let he bought x tickets. ATQ,
4.50x = 36
So, he can buy 8 tickets.
Answer:
4.34
Step-by-step explanation:
2.48/40=0.062 per ounce
0.062 x 70 = 4.32 for 70 ounces
Answer:
2(5x + 2)
Step-by-step explanation:
The nearest degree would be 40
