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Assume the expression is:
2sin²(x) + cos²(x) = 1
Use this identity to work out the problem: cos²(x) = 1 - sin²(x)
Then:
2sin²(x) + 1 - sin²(x) = 1
sin²(x) + 1 = 1
sin²(x) = 0
sin(x) = 0
Therefore, the solutions are:
x = πk radians where k belongs to the set of integers
In degrees, we obtain:
x = 180l° where l belongs to the set of integers
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Find the second derivative of y equals sin sqaured x?
y = sin2(x) y' = 2sin(x)cos(x) y'' = 2 [ cos(x)cos(x) + sin(x)(-sin(x)) ] = 2 [ cos2(x) - sin2(x) ] = 2 [ 1 - sin2(x) - sin2(x) ] = 2 [ 1 - 2sin2(x) ]
Find all degree solutions 2sin2 6x plus 3sin6x plus 1 equals 0?
2sin2(6x) + 3sin(6x) + 1 = 0 Solving the quadratic, sin(6x) = -1 or sin (6x) = -0.5 sin(6x) = -1 => 6x = 45+60n degrees for integer n sin(6x) = -0.5 => 6x = 35+60n or 55+60n degrees for integer n.
Find the solution 3x-3y equals 12 and 3x plus y equals 8?
70000000y=35t
Find solution for N equals 3?
N = 3. That really is all there is to it.
Given 2sin s equals cos s find all possible values of sin s?
2sin s = cos s; whence, 4sin2 s = cos2 s = 1 - sin2s, and 5sin2 s = 1. Therefore sin s = ±√0.2 = 0.4472, approx. Check: cos2 s = 1 - 0.2 = 0.8, whence, cos s = ±√0.8 = ±2√0.2 = 2 sin s.
Find the second derivative of y equals sin sqaured x?
y = sin2(x) y' = 2sin(x)cos(x) y'' = 2 [ cos(x)cos(x) + sin(x)(-sin(x)) ] = 2 [ cos2(x) - sin2(x) ] = 2 [ 1 - sin2(x) - sin2(x) ] = 2 [ 1 - 2sin2(x) ]
Find all degree solutions 2sin2 6x plus 3sin6x plus 1 equals 0?
2sin2(6x) + 3sin(6x) + 1 = 0 Solving the quadratic, sin(6x) = -1 or sin (6x) = -0.5 sin(6x) = -1 => 6x = 45+60n degrees for integer n sin(6x) = -0.5 => 6x = 35+60n or 55+60n degrees for integer n.
What is the second derivative of y equals 2sinx cosx?
y = 2sin(x)cos(x)Use the product rule: uv' + vu' where u is 2sin(x) and v is cos(x) to find first derivative:y' = 2sin(x)(-sin(x)) + cos(x)2cos(x)Simplify:y' = 2cos2(x)-2sin2(x)y' = 2(cos2(x)-sin2(x))Use trig identity cos(2x) = cos2(x)-sin2(x):y' = 2cos(2x)Take second derivative using chain rule:y'' = 2(-sin(2x)cos(2x))Simplify:y'' = -2sin(2x)(2)Simplify:y'' = -4sin(2x)y'' = -4sin(2x)
How would you find a solution to y equals 3x-5x?
8
Find the solution 3x-3y equals 12 and 3x plus y equals 8?
70000000y=35t
Find solution for N equals 3?
N = 3. That really is all there is to it.
Given 2sin s equals cos s find all possible values of sin s?
2sin s = cos s; whence, 4sin2 s = cos2 s = 1 - sin2s, and 5sin2 s = 1. Therefore sin s = ±√0.2 = 0.4472, approx. Check: cos2 s = 1 - 0.2 = 0.8, whence, cos s = ±√0.8 = ±2√0.2 = 2 sin s.
By inspection find a particular solution to y'' plus 2y equals 10?
y = 5
How many solutions are there in the equation 2x equals 10?
There is one solution. To find it, divide both sides of the equation by 2. This leaves you with x=5, where 5 is your solution.
What is the solution of x plus y equals 5?
You have two unknown variables, x and y. You therefore need at least two independent equations to find a solution.
How do you solve 3a plus b equals 1 and a plus b equals to find a common solution?
The second equation is not complete and there is not sufficient information for a solution. It would make no sense for me to guess what a + b equals since, in that case, I may as well start posting my own questions and answering them!
Find all radian solutions in the interval 0 is less than or equal to x less than 2pi 2sin2 x - 6sinx - 1 equals 0?
2sin2x - 6sinx - 1 = 0Therefore, using the quadratic equation,sinx = (3-sqrt(11)/2 = -0.1583 or sinx > 3.The latter solution is not possible since |sin(x)| cannot exceed 1.arcsin(-0.1583) = -0.1590 radiansso x = 2pi - 0.1590 = 6.1242 radiansalso x = pi + 0.1590 = 3.3006 radians
