Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation 4*x=0
-
Equation 7*x=0
-
Equation 4x+3(x-7)=5
-
Equation 3x-2=x+4
- Express {x} in terms of y where:
- 14*x-17*y=-4
- 18*x-10*y=-9
- 6*x+16*y=-7
- 2*x-16*y=14
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Identical expressions
- sin(pi*x/ seven)= zero
- sinus of ( Pi multiply by x divide by 7) equally 0
- sinus of ( Pi multiply by x divide by seven) equally zero
- sin(pix/7)=0
- sinpix/7=0
- sin(pi*x/7)=O
- sin(pi*x divide by 7)=0
sin(pi*x/7)=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$\sin{\left(\frac{\pi x}{7} \right)} = 0$$
- this is the simplest trigonometric equation
We get:
$$\sin{\left(\frac{\pi x}{7} \right)} = 0$$
This equation is transformed to
$$\frac{\pi x}{7} = 2 \pi n + \operatorname{asin}{\left(0 \right)}$$
$$\frac{\pi x}{7} = 2 \pi n - \operatorname{asin}{\left(0 \right)} + \pi$$
Or
$$\frac{\pi x}{7} = 2 \pi n$$
$$\frac{\pi x}{7} = 2 \pi n + \pi$$
, where n - is a integer
Divide both parts of the equation by
$$\frac{\pi}{7}$$
we get the answer:
$$x_{1} = 14 n$$
$$x_{2} = \frac{7 \left(2 \pi n + \pi\right)}{\pi}$$
$$\sin{\left(\frac{\pi x}{7} \right)} = 0$$
- this is the simplest trigonometric equation
with the change of sign in 0
We get:
$$\sin{\left(\frac{\pi x}{7} \right)} = 0$$
This equation is transformed to
$$\frac{\pi x}{7} = 2 \pi n + \operatorname{asin}{\left(0 \right)}$$
$$\frac{\pi x}{7} = 2 \pi n - \operatorname{asin}{\left(0 \right)} + \pi$$
Or
$$\frac{\pi x}{7} = 2 \pi n$$
$$\frac{\pi x}{7} = 2 \pi n + \pi$$
, where n - is a integer
Divide both parts of the equation by
$$\frac{\pi}{7}$$
we get the answer:
$$x_{1} = 14 n$$
$$x_{2} = \frac{7 \left(2 \pi n + \pi\right)}{\pi}$$
Numerical answer
[src]
x1 = -63.0
x2 = -77.0
x3 = -84.0
x4 = -35.0
x5 = 35.0
x6 = 0.0
x7 = 14.0
x8 = -21.0
x9 = 21.0
x10 = 56.0
x11 = 49.0
x12 = 7.0
x13 = 91.0
x14 = -56.0
x15 = 63.0
x16 = 70.0
x17 = -70.0
x18 = 28.0
x19 = 42.0
x20 = -98.0
x21 = 77.0
x22 = -14.0
x23 = 84.0
x24 = -28.0
x25 = -7.0
x26 = 98.0
x27 = -42.0
x28 = -49.0
x29 = -91.0
x29 = -91.0