Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation -7x=13-2(8x-7)
-
Equation e^x=1
-
Equation 8+x^3=0
-
Equation sin(x/2)=0
- Express {x} in terms of y where:
- 1*x+5*y=-11
- 20*x-8*y=13
- -16*x+7*y=-5
- -16*x-14*y=-9
- Graphing y =:
- sin(x/2)
- Derivative of:
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sin(x/2)
- Integral of d{x}:
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sin(x/2)
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Identical expressions
- sin(x/ two)= zero
- sinus of (x divide by 2) equally 0
- sinus of (x divide by two) equally zero
- sinx/2=0
- sin(x/2)=O
- sin(x divide by 2)=0
-
Similar expressions
- 2*sin(x)/2=1-cos(x)
- sinx+(cosx/2-sinx/2)(cox/2+sinx/2)=0
- sin(x/2-П/6)+1=0
sin(x/2)=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$\sin{\left(\frac{x}{2} \right)} = 0$$
- this is the simplest trigonometric equation
We get:
$$\sin{\left(\frac{x}{2} \right)} = 0$$
This equation is transformed to
$$\frac{x}{2} = 2 \pi n + \operatorname{asin}{\left(0 \right)}$$
$$\frac{x}{2} = 2 \pi n - \operatorname{asin}{\left(0 \right)} + \pi$$
Or
$$\frac{x}{2} = 2 \pi n$$
$$\frac{x}{2} = 2 \pi n + \pi$$
, where n - is a integer
Divide both parts of the equation by
$$\frac{1}{2}$$
we get the answer:
$$x_{1} = 4 \pi n$$
$$x_{2} = 4 \pi n + 2 \pi$$
$$\sin{\left(\frac{x}{2} \right)} = 0$$
- this is the simplest trigonometric equation
with the change of sign in 0
We get:
$$\sin{\left(\frac{x}{2} \right)} = 0$$
This equation is transformed to
$$\frac{x}{2} = 2 \pi n + \operatorname{asin}{\left(0 \right)}$$
$$\frac{x}{2} = 2 \pi n - \operatorname{asin}{\left(0 \right)} + \pi$$
Or
$$\frac{x}{2} = 2 \pi n$$
$$\frac{x}{2} = 2 \pi n + \pi$$
, where n - is a integer
Divide both parts of the equation by
$$\frac{1}{2}$$
we get the answer:
$$x_{1} = 4 \pi n$$
$$x_{2} = 4 \pi n + 2 \pi$$
Sum and product of roots
[src]
sum
2*pi
$$2 \pi$$
=
2*pi
$$2 \pi$$
product
0*2*pi
$$0 \cdot 2 \pi$$
=
0
$$0$$
0
Numerical answer
[src]
x1 = 69.1150383789755
x2 = -50.2654824574367
x3 = 25.1327412287183
x4 = 18.8495559215388
x5 = 56.5486677646163
x6 = 94.2477796076938
x7 = -69.1150383789755
x8 = -81.6814089933346
x9 = 50.2654824574367
x10 = 43.9822971502571
x11 = 87.9645943005142
x12 = -43.9822971502571
x13 = -6.28318530717959
x14 = -18.8495559215388
x15 = 81.6814089933346
x16 = -62.8318530717959
x17 = 6.28318530717959
x18 = -94.2477796076938
x19 = -12.5663706143592
x20 = -226.194671058465
x21 = 75.398223686155
x22 = -75.398223686155
x23 = -31.4159265358979
x24 = 62.8318530717959
x25 = -56.5486677646163
x26 = -106.814150222053
x27 = -87.9645943005142
x28 = 37.6991118430775
x29 = -25.1327412287183
x30 = 100.530964914873
x31 = -37.6991118430775
x32 = 0.0
x33 = 31.4159265358979
x34 = 12.5663706143592
x35 = -100.530964914873
x35 = -100.530964914873
The graph