Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation 25*x^3-10*x^2+x=0
-
Equation 2x^2-x-1=x^2-5x-(-1-x^2)
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Equation 2^x=5
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Equation (x-10)^2=(x+4)^2
- Express {x} in terms of y where:
- 15*x+12*y=-19
- -19*x-20*y=-4
- -18*x+12*y=-8
- -14*x+4*y=-16
- Derivative of:
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sin(pi*x/4)
- Integral of d{x}:
- sin(pi*x/4)
- Limit of the function:
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sin(pi*x/4)
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Identical expressions
- sin(pi*x/ four)=sqrt two /2
- sinus of ( Pi multiply by x divide by 4) equally square root of 2 divide by 2
- sinus of ( Pi multiply by x divide by four) equally square root of two divide by 2
- sin(pi*x/4)=√2/2
- sin(pix/4)=sqrt2/2
- sinpix/4=sqrt2/2
- sin(pi*x divide by 4)=sqrt2 divide by 2
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Similar expressions
- cos(x/2)=sqrt(2)/2
- cos(6x)=sqrt(2)/2
- sin(pi*x)/4=sqrt(2)/2
- cos*pi*(x+1)/4=sqrt(2)/2
- sin((pi*x)/4)=1
sin(pi*x/4)=sqrt2/2 equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
___ /pi*x\ \/ 2 sin|----| = ----- \ 4 / 2
$$\sin{\left(\frac{\pi x}{4} \right)} = \frac{\sqrt{2}}{2}$$
Detail solution
Given the equation
$$\sin{\left(\frac{\pi x}{4} \right)} = \frac{\sqrt{2}}{2}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$\frac{\pi x}{4} = 2 \pi n + \operatorname{asin}{\left(\frac{\sqrt{2}}{2} \right)}$$
$$\frac{\pi x}{4} = 2 \pi n - \operatorname{asin}{\left(\frac{\sqrt{2}}{2} \right)} + \pi$$
Or
$$\frac{\pi x}{4} = 2 \pi n + \frac{\pi}{4}$$
$$\frac{\pi x}{4} = 2 \pi n + \frac{3 \pi}{4}$$
, where n - is a integer
Divide both parts of the equation by
$$\frac{\pi}{4}$$
we get the answer:
$$x_{1} = \frac{4 \left(2 \pi n + \frac{\pi}{4}\right)}{\pi}$$
$$x_{2} = \frac{4 \left(2 \pi n + \frac{3 \pi}{4}\right)}{\pi}$$
$$\sin{\left(\frac{\pi x}{4} \right)} = \frac{\sqrt{2}}{2}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$\frac{\pi x}{4} = 2 \pi n + \operatorname{asin}{\left(\frac{\sqrt{2}}{2} \right)}$$
$$\frac{\pi x}{4} = 2 \pi n - \operatorname{asin}{\left(\frac{\sqrt{2}}{2} \right)} + \pi$$
Or
$$\frac{\pi x}{4} = 2 \pi n + \frac{\pi}{4}$$
$$\frac{\pi x}{4} = 2 \pi n + \frac{3 \pi}{4}$$
, where n - is a integer
Divide both parts of the equation by
$$\frac{\pi}{4}$$
we get the answer:
$$x_{1} = \frac{4 \left(2 \pi n + \frac{\pi}{4}\right)}{\pi}$$
$$x_{2} = \frac{4 \left(2 \pi n + \frac{3 \pi}{4}\right)}{\pi}$$
Numerical answer
[src]
x1 = 1.0
x2 = -93.0
x3 = 43.0
x4 = -31.0
x5 = 35.0
x6 = -69.0
x7 = 25.0
x8 = -5.0
x9 = -71.0
x10 = 27.0
x11 = 81.0
x12 = -7.0
x13 = 67.0
x14 = 19.0
x15 = 83.0
x16 = -29.0
x17 = 89.0
x18 = -37.0
x19 = -101.0
x20 = 3.0
x21 = 131.0
x22 = 49.0
x23 = -55.0
x24 = 107.0
x25 = 97.0
x26 = -47.0
x27 = -13.0
x28 = -85.0
x29 = -63.0
x30 = -77.0
x31 = -45.0
x32 = 17.0
x33 = -21.0
x34 = -39.0
x35 = -15.0
x36 = -79.0
x37 = 91.0
x38 = 115.0
x39 = -53.0
x40 = 73.0
x41 = 59.0
x42 = 99.0
x43 = -87.0
x44 = -23.0
x45 = -95.0
x46 = 9.0
x47 = 57.0
x48 = 11.0
x49 = 33.0
x50 = 65.0
x51 = -61.0
x52 = 75.0
x53 = 41.0
x54 = 51.0
x55 = 123.0
x55 = 123.0