Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation x^2=-100
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Equation -7*x=4
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Equation 10x-2(4x-5)=2x+10
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Equation -4/7*x^2+28=0
- Express {x} in terms of y where:
- 4*x-4*y=-19
- 5*x-4*y=14
- -16*x+18*y=9
- 4*x-1*y=12
- Limit of the function:
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tan(pi*x/4)
- Sum of series:
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-1
- Integral of d{x}:
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-1
- Derivative of:
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-1
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Identical expressions
- tan(pi*x/ four)=- one
- tangent of ( Pi multiply by x divide by 4) equally minus 1
- tangent of ( Pi multiply by x divide by four) equally minus one
- tan(pix/4)=-1
- tanpix/4=-1
- tan(pi*x divide by 4)=-1
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Similar expressions
- tan(pi*x/4)=+1
tan(pi*x/4)=-1 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$\tan{\left(\frac{\pi x}{4} \right)} = -1$$
- this is the simplest trigonometric equation
This equation is transformed to
$$\frac{\pi x}{4} = \pi n + \operatorname{atan}{\left(-1 \right)}$$
Or
$$\frac{\pi x}{4} = \pi n - \frac{\pi}{4}$$
, where n - is a integer
Divide both parts of the equation by
$$\frac{\pi}{4}$$
we get the answer:
$$x_{1} = \frac{4 \left(\pi n - \frac{\pi}{4}\right)}{\pi}$$
$$\tan{\left(\frac{\pi x}{4} \right)} = -1$$
- this is the simplest trigonometric equation
This equation is transformed to
$$\frac{\pi x}{4} = \pi n + \operatorname{atan}{\left(-1 \right)}$$
Or
$$\frac{\pi x}{4} = \pi n - \frac{\pi}{4}$$
, where n - is a integer
Divide both parts of the equation by
$$\frac{\pi}{4}$$
we get the answer:
$$x_{1} = \frac{4 \left(\pi n - \frac{\pi}{4}\right)}{\pi}$$
Numerical answer
[src]
x1 = -37.0
x2 = 19.0
x3 = 39.0
x4 = -53.0
x5 = 15.0
x6 = -65.0
x7 = 95.0
x8 = -9.0
x9 = -97.0
x10 = -21.0
x11 = -57.0
x12 = 83.0
x13 = 3.0
x14 = 55.0
x15 = -29.0
x16 = -77.0
x17 = 63.0
x18 = 99.0
x19 = -85.0
x20 = 51.0
x21 = 91.0
x22 = 7.0
x23 = 75.0
x24 = 35.0
x25 = -5.0
x26 = -61.0
x27 = 27.0
x28 = 47.0
x29 = -13.0
x30 = -101.0
x31 = -93.0
x32 = 71.0
x33 = 31.0
x34 = 67.0
x35 = -41.0
x36 = -1.0
x37 = 59.0
x38 = 11.0
x39 = -69.0
x40 = 43.0
x41 = 23.0
x42 = -17.0
x43 = -81.0
x44 = -73.0
x45 = 87.0
x46 = 79.0
x47 = -25.0
x48 = -49.0
x49 = -45.0
x50 = -33.0
x51 = -89.0
x51 = -89.0
The graph