Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation x/4+x=12
-
Equation 5^x=6-x
-
Equation -5+2x=-2x-7
-
Equation x^2-18=7*x
- Express {x} in terms of y where:
- -16*x-9*y=-1
- -18*x-13*y=2
- 8*x-4*y=10
- -6*x-11*y=-20
- Sum of series:
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-1
- Derivative of:
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-1
- Integral of d{x}:
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-1
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Identical expressions
- sin((pi*x)/ four)=- one
- sinus of (( Pi multiply by x) divide by 4) equally minus 1
- sinus of (( Pi multiply by x) divide by four) equally minus one
- sin((pix)/4)=-1
- sinpix/4=-1
- sin((pi*x) divide by 4)=-1
-
Similar expressions
- sin((pi*x)/4)=+1
- sin((pi*x))/4=sqrt2/2
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
$$\frac{\pi x}{4} = 2 \pi n - \frac{\pi}{2}$$
$$\frac{\pi x}{4} = 2 \pi n + \frac{3 \pi}{2}$$
, where n - is a integer
Divide both parts of the equation by
$$\frac{\pi}{4}$$
we get the answer:
$$x_{1} = \frac{4 \left(2 \pi n - \frac{\pi}{2}\right)}{\pi}$$
$$x_{2} = \frac{4 \left(2 \pi n + \frac{3 \pi}{2}\right)}{\pi}$$
$$\sin{\left(\frac{\pi x}{4} \right)} = -1$$
- 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
$$\frac{\pi x}{4} = 2 \pi n - \frac{\pi}{2}$$
$$\frac{\pi x}{4} = 2 \pi n + \frac{3 \pi}{2}$$
, where n - is a integer
Divide both parts of the equation by
$$\frac{\pi}{4}$$
we get the answer:
$$x_{1} = \frac{4 \left(2 \pi n - \frac{\pi}{2}\right)}{\pi}$$
$$x_{2} = \frac{4 \left(2 \pi n + \frac{3 \pi}{2}\right)}{\pi}$$
Sum and product of roots
[src]
sum
-2 + 6
$$-2 + 6$$
=
4
$$4$$
product
-2*6
$$- 12$$
=
-12
$$-12$$
-12
Numerical answer
[src]
x1 = 6.0
x2 = -82.0
x3 = 38.0000006559158
x4 = -10.0000006396378
x5 = -50.0
x6 = 78.0
x7 = 5.99999936036215
x8 = -42.0
x9 = -1.99999934408419
x10 = -81.9999993440842
x11 = 22.0
x12 = -73.9999993440842
x13 = 14.0000006559158
x14 = -58.0000006396378
x15 = -90.0000006396378
x16 = 30.0000006559158
x17 = 14.0
x18 = 101.999999360362
x19 = -89.9999993440842
x20 = -26.0000006396378
x21 = 54.0
x22 = 54.0000006559158
x23 = -50.0000006396378
x24 = 29.9999993603622
x25 = -66.0
x26 = -82.0000006396378
x27 = 62.0
x28 = 85.9999993603622
x29 = -34.0000006396378
x30 = -41.9999993440842
x31 = -33.9999993440842
x32 = -58.0
x33 = -18.0000006396378
x34 = 69.9999993603622
x35 = 30.0
x36 = 13.9999993603622
x37 = 6.00000065591581
x38 = 77.9999993603622
x39 = -10.0
x40 = -17.9999993440842
x41 = 53.9999993603622
x42 = 37.9999993603622
x43 = 46.0
x44 = 46.0000006559158
x45 = -65.9999993440842
x46 = 45.9999993603622
x47 = 94.0
x48 = 38.0
x49 = 94.0000006559158
x50 = 21.9999993603622
x51 = 93.9999993603622
x52 = -57.9999993440842
x53 = 86.0
x54 = -49.9999993440842
x55 = 62.0000006559158
x56 = -98.0
x57 = -90.0
x58 = -9.99999934408419
x59 = -2.0
x60 = -74.0000006396378
x61 = -66.0000006396378
x62 = 61.9999993603622
x63 = 86.0000006559158
x64 = 70.0
x65 = -42.0000006396378
x66 = -98.0000006396378
x67 = 78.0000006559158
x68 = -97.9999993440842
x69 = -18.0
x70 = -74.0
x71 = 70.0000006559158
x72 = -25.9999993440842
x73 = -34.0
x74 = -26.0
x75 = 22.0000006559158
x76 = -2.00000063963785
x76 = -2.00000063963785
The graph