Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation tan(x)=-1/2
-
Equation 1*(x-1)*(x-3)=0
-
Equation 5x+12=8x+30
-
Equation x^2-11*x+30=0
- Express {x} in terms of y where:
- -2*x-19*y=3
- -2*x+18*y=13
- -2*x-15*y=-1
- 10*x-2*y=11
-
Identical expressions
- -4sin(zero ,5x)= zero
- minus 4 sinus of (0,5x) equally 0
- minus 4 sinus of (zero ,5x) equally zero
- -4sin0,5x=0
- -4sin(0,5x)=O
-
Similar expressions
- 4sin(0,5x)=0
-4sin(0,5x)=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$- 4 \sin{\left(\frac{x}{2} \right)} = 0$$
- this is the simplest trigonometric equation
We get:
$$- 4 \sin{\left(\frac{x}{2} \right)} = 0$$
The equation is transformed to
$$\sin{\left(\frac{x}{2} \right)} = 0$$
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:
$$x_{1} = 4 \pi n$$
$$x_{2} = 4 \pi n + 2 \pi$$
$$- 4 \sin{\left(\frac{x}{2} \right)} = 0$$
- this is the simplest trigonometric equation
with the change of sign in 0
We get:
$$- 4 \sin{\left(\frac{x}{2} \right)} = 0$$
Divide both parts of the equation by -4
The equation is transformed to
$$\sin{\left(\frac{x}{2} \right)} = 0$$
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 = 31.4159265358979
x2 = -12.5663706143592
x3 = 75.398223686155
x4 = -69.1150383789755
x5 = -50.2654824574367
x6 = -56.5486677646163
x7 = -62.8318530717959
x8 = -6.28318530717959
x9 = 6.28318530717959
x10 = 62.8318530717959
x11 = -25.1327412287183
x12 = 94.2477796076938
x13 = -37.6991118430775
x14 = -100.530964914873
x15 = -43.9822971502571
x16 = 25.1327412287183
x17 = 87.9645943005142
x18 = 43.9822971502571
x19 = -31.4159265358979
x20 = -94.2477796076938
x21 = 18.8495559215388
x22 = -106.814150222053
x23 = -18.8495559215388
x24 = 12.5663706143592
x25 = -226.194671058465
x26 = 81.6814089933346
x27 = -75.398223686155
x28 = -81.6814089933346
x29 = 50.2654824574367
x30 = -87.9645943005142
x31 = 56.5486677646163
x32 = 37.6991118430775
x33 = 100.530964914873
x34 = 69.1150383789755
x35 = 0.0
x35 = 0.0