Mister Exam
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How to use it?
- Equation:
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Equation x+12=5
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Equation x^2+x=12
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Equation x^4=(x-56)^2
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Equation -6x+2=-x+22
- Express {x} in terms of y where:
- 18*x+19*y=7
- 8*x-13*y=-12
- 1*x+6*y=6
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Identical expressions
- sin((pi*x)/ four)= one
- sinus of (( Pi multiply by x) divide by 4) equally 1
- sinus of (( Pi multiply by x) divide by four) equally one
- sin((pix)/4)=1
- sinpix/4=1
- sin((pi*x) divide by 4)=1
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Similar expressions
- 4*(|x|)+1/(|x|)=4*sin(pi*x/4)
- sin(pi*x/4)+1=cos(pi*x/8)+sqrt(2)*cos(pi*x/8-pi/4)
sin((pi*x)/4)=1 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$\sin{\left(\frac{\pi x}{4} \right)} = 1$$
- this is the simplest trigonometric equation
This equation is transformed to
$$\frac{\pi x}{4} = 2 \pi n + \operatorname{asin}{\left(1 \right)}$$
$$\frac{\pi x}{4} = 2 \pi n - \operatorname{asin}{\left(1 \right)} + \pi$$
Or
$$\frac{\pi x}{4} = 2 \pi n + \frac{\pi}{2}$$
$$\frac{\pi x}{4} = 2 \pi n + \frac{\pi}{2}$$
, where n - is a integer
Divide both parts of the equation by
$$\frac{\pi}{4}$$
we get the answer:
$$x_{1} = \frac{4 \left(2 \pi n + \frac{\pi}{2}\right)}{\pi}$$
$$x_{2} = \frac{4 \left(2 \pi n + \frac{\pi}{2}\right)}{\pi}$$
$$\sin{\left(\frac{\pi x}{4} \right)} = 1$$
- this is the simplest trigonometric equation
This equation is transformed to
$$\frac{\pi x}{4} = 2 \pi n + \operatorname{asin}{\left(1 \right)}$$
$$\frac{\pi x}{4} = 2 \pi n - \operatorname{asin}{\left(1 \right)} + \pi$$
Or
$$\frac{\pi x}{4} = 2 \pi n + \frac{\pi}{2}$$
$$\frac{\pi x}{4} = 2 \pi n + \frac{\pi}{2}$$
, where n - is a integer
Divide both parts of the equation by
$$\frac{\pi}{4}$$
we get the answer:
$$x_{1} = \frac{4 \left(2 \pi n + \frac{\pi}{2}\right)}{\pi}$$
$$x_{2} = \frac{4 \left(2 \pi n + \frac{\pi}{2}\right)}{\pi}$$
Numerical answer
[src]
x1 = 74.0
x2 = 2.0
x3 = 49.9999993603622
x4 = -78.0
x5 = 18.0
x6 = -38.0
x7 = -70.0
x8 = 58.0
x9 = -53.9999993440842
x10 = 10.0000006559158
x11 = 26.0000006559158
x12 = -30.0000006396378
x13 = 82.0000006559158
x14 = 66.0
x15 = 73.9999993603622
x16 = 34.0000006559158
x17 = -45.9999993440842
x18 = 17.9999993603622
x19 = -94.0000006396378
x20 = 42.0000006559158
x21 = 81.9999993603622
x22 = 82.0
x23 = -62.0
x24 = 50.0000006559158
x25 = 89.9999993603622
x26 = 42.0
x27 = -69.9999993440842
x28 = -70.0000006396378
x29 = 58.0000006559158
x30 = -22.0
x31 = 26.0
x32 = -85.9999993440842
x33 = 50.0
x34 = 65.9999993603622
x35 = -86.0
x36 = -61.9999993440842
x37 = 33.9999993603622
x38 = 18.0000006559158
x39 = -29.9999993440842
x40 = 41.9999993603622
x41 = -94.0
x42 = 74.0000006559158
x43 = -22.0000006396378
x44 = -6.00000063963785
x45 = 90.0000006559158
x46 = 98.0000006559158
x47 = -46.0000006396378
x48 = -13.9999993440842
x49 = -78.0000006396378
x50 = -21.9999993440842
x51 = -14.0
x52 = -54.0000006396378
x53 = -30.0
x54 = -86.0000006396378
x55 = 10.0
x56 = -77.9999993440842
x57 = -46.0
x58 = -37.9999993440842
x59 = -101.999999344084
x60 = -62.0000006396378
x61 = -5.99999934408419
x62 = -93.9999993440842
x63 = 66.0000006559158
x64 = 97.9999993603622
x65 = 98.0
x66 = 34.0
x67 = 2.00000065591581
x68 = 90.0
x69 = -38.0000006396378
x70 = 1.99999936036215
x71 = 25.9999993603622
x72 = 57.9999993603622
x73 = -6.0
x74 = -54.0
x75 = 9.99999936036215
x76 = -14.0000006396378
x76 = -14.0000006396378
The graph