Find all solutions of the equation:
2 cosx + sqrt2 = 0
A) x = ð/4 + 2nð or x = 7ð/4 + 2nð
B) x = 3ð/4 + 2nð or x = 5ð/4 + 2nð
C) x = ð/4 + nð or x = 7ð/4 + nð
D) x = 3ð/4 + nð or x = 5ð/4 + nð
this is in 3 grade?
that is NOT a 3rd grade equation, but nice try. I would help you, but you are not in third grade, there for you can figure it out. I am in fourth grade Cambridge and I only know that because I looked it up. and when you first look it up, you will find yourself!!!! you have to go to the calculator... if you are even allowed to use it in... what twelfth grade?
To find the solutions of the equation 2cos(x) + √2 = 0, we can use the fact that the cosine function has a range of -1 to 1.
First, we subtract √2 from both sides of the equation:
2cos(x) = -√2
Then, we divide both sides by 2:
cos(x) = -√2/2
Now, we need to find the angles whose cosine is -√2/2. Since the cosine is equal to the adjacent side divided by the hypotenuse in a right triangle, we can use the unit circle to find these angles.
The unit circle is a circle with a radius of 1 centered at the origin (0,0) in the Cartesian coordinate system. We can consider different points on the unit circle and use the coordinates of these points to find the corresponding angle.
For the cosine of an angle to equal -√2/2, the x-coordinate of the point on the unit circle should be -√2/2.
The unit circle has two points where x = -√2/2:
1) (-√2/2, 1/2) at an angle of π/4 radians or 45 degrees
2) (-√2/2, -1/2) at an angle of 7π/4 radians or 315 degrees
Since the cosine function has a period of 2π, we can add multiples of 2π to these angles to find all possible solutions.
The solutions to the equation 2cos(x) + √2 = 0 are:
x = π/4 + 2nπ or x = 7π/4 + 2nπ
where n is an integer.
Therefore, the correct answer is A) x = π/4 + 2nπ or x = 7π/4 + 2nπ.