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: 15n³-105n²+2n+16/6n²-42n
Step-by-step explanation:
n+8/3n²-21n +5n/2
2(n+8)+5n(3n²-21n)/2(3n²-21n)
2n+16+15n³-105n²/6n²-42n
15n³-105n²+2n+16/6n²-42n
For the limit approaching 3 from the right, you want to follow the line to the right of x = 3. From the graph you're describing it sounds like that's y = -3.
The RHS limit is -3 even though f(3) = 7
Answer:
if this is a fraction, then negative 5 over a⁶
You are correct. The scale factor is 1/5 = 0.2
Nice work.
