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:
h= -2
Step-by-step explanation:
How to solve your question
Your question is
ℎ
=
(
−
4
)
−
ℎ
h=(-4)-h
h=(−4)−h
Solve
1
ℎ − 4
h=-h-4
h=−h−4
2. Subtract from both sides of the equation
3. Simplify
4. Divide both sides of the equation by the same term
5. Simplify
Solution
ℎ = −2
Answer:
In bold below.
Step-by-step explanation:
let the shorter leg be x units long, then:
longer leg = x+4
and hypotenuse = x + x + 4 - 8 = 2x - 4 units.
By Pythagoras:
(2x - 4)^2 = x^2 + (x + 4)^2
4x^2 - 16x + 16 = x^2 + x^2 +8x + 16
2x^2 - 24x = 0
2x(x - 12) = 0
x = 12.
So the shorter leg = 12 units
Longer leg = 4 + 12 = 16 units and
Hypotenuse = 12 + 16 - 8 = 20 units.
see diagram in attachment
a rhombus is a 4 sided figure with 4 equal length sides
so if we can find the length of 1 side and multiply it by 4, we get the perimiter
you can draw 2 lines to make 4 similar triangles
we can see that you can use pythagorean rule to get the length of the hypotonuse of one triangle so so perimiter is 4*5=20 units
or you can use distance formula which is basically the pythatorean theorm
from W to X, that is from (-3,1) to (1,4)
4*5=20, so perimiter is 20 units
4cm+350mm= 40cm
Step-by-step explanation:
when you convert 360mm it's 36cm and then you add 4cm+36cm which equals 40cm.