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:
1) 8
Step-by-step explanation:
3+2 is 5
4^2 is 16
16×5=80
2×5=10
80÷10=8
Step-by-step explanation:
f(x) = 9 * 81^x
When x = -1/2,
f(-1/2) = 9 * 81^(-1/2) = 9 * (1/9) = 1.
We are given pattern 615,605,595.
Let us check differences of second term - first term and
Third term - second term
Second term - first term = 605 - 615 = -10.
Third term - second term = 595 - 605 = -10.
So, each time 10 is being subtracted from previous term.
So, the sequnace would be
<h3>615, 605, 595, <u>585</u>, <u>575</u>, <u>565.</u></h3>
