It equals zero negative plus positive equals zero
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
-4(x+10)-6=-3(x-2)
-4x-40-6=-3x+6
-4x-46=-3x+6
-4x-46+46=-3x+6+46
-4x=-3x+52
-4x+3x=-3x+3x+52
-x=52
(-x/-1)=(52/-1)
x=-52
The absolute function will be f(x) = | x - 5 | - 4.
<h3 /><h3>What is an absolute function?</h3>
The absolute function is also known as the mode function. The value of the absolute function is always positive.
The absolute function is given as
f(x) = | x - h | + k
Where h,k is the vertex of the absolute function.
f(x) = | x - 5 | - 4
Therefore the absolute function will be f(x) = | x - 5 | - 4.
More about the absolute function link is given below.
brainly.com/question/10664936
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