It looks like the given equation is
sin(2x) - sin(2x) cos(2x) = sin(4x)
Recall the double angle identity for sine:
sin(2x) = 2 sin(x) cos(x)
which lets us rewrite the equation as
sin(2x) - sin(2x) cos(2x) = 2 sin(2x) cos(2x)
Move everything over to one side and factorize:
sin(2x) - sin(2x) cos(2x) - 2 sin(2x) cos(2x) = 0
sin(2x) - 3 sin(2x) cos(2x) = 0
sin(2x) (1 - 3 cos(2x)) = 0
Then we have two families of solutions,
sin(2x) = 0 or 1 - 3 cos(2x) = 0
sin(2x) = 0 or cos(2x) = 1/3
[2x = arcsin(0) + 2nπ or 2x = π - arcsin(0) + 2nπ]
… … … or [2x = arccos(1/3) + 2nπ or 2x = -arccos(1/3) + 2nπ]
(where n is any integer)
[2x = 2nπ or 2x = π + 2nπ]
… … … or [2x = arccos(1/3) + 2nπ or 2x = -arccos(1/3) + 2nπ]
[x = nπ or x = π/2 + nπ]
… … … or [x = 1/2 arccos(1/3) + nπ or x = -1/2 arccos(1/3) + nπ]
Answer:
Step-by-step explanation:
This is a right triangle problem using Pythagorean's Theorem. The height of the building to the edge of the roof is 20 feet. If the ladder has to be 1/4 the height of the wall away from the building, then the base of the right triangle is 1/4 of 20 which is 5 feet. The ladder itself is the hypotenuse of the triangle, for which we are seeking a length. Use Pythagorean's Theorem:
and
and
so
c = 20.6 ft
Answer:
x = -2, y = -9
Step-by-step explanation:
You can substitute the value of y into y. The first equation shows that y is equal to 4x -1, so we can switch this with the y in the second equation.
y = 2x -5 will become
4x - 1 = 2x - 5
Add 5 to both sides
4x + 4 = 2x
Subtract 4x from both sides
4 = -2x
Divide both sides by -2
-2 = x
Now we plug this number into an equation to find y.
y = 4x - 1 becomes
y = 4(-2) - 1
Simplifying it, we have:
y = -8 - 1
y = -9
Is there any way you can add the graph on here?
Answer:
x = 6, y = 17
Step-by-step explanation:
These equations are both equal to y.
Substitute 3x - 1 in the y value of the first equation.
3x - 1 = 2x + 5
Subtract 2x.
x - 1 = 5
Add 1 to both sides
x = 6
Then substitute this x value into the first equation.
y = 2x + 5
y = 2(6) + 5 = 12 + 5 = 17
