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- Equation:
-
Equation cos*((pi(4x+48))/4)=-(sqrt(2)/2)
- Equation 36^x+1+35*6^x-1=0
-
Equation 13x+8=27x+18
- Equation sin(pi(x+4)/6)=-0.5
- Express {x} in terms of y where:
- (x^2+y^2-1)^3+x^2*y^3=0
- -1*x-19*y=-10
- 5*x+5*y=20
- 4*x-16*y=6
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Identical expressions
- cos*((pi(four x+ forty-eight))/4)=-(sqrt(two)/ two)
- co sinus of e of multiply by (( Pi (4x plus 48)) divide by 4) equally minus ( square root of (2) divide by 2)
- co sinus of e of multiply by (( Pi (four x plus forty minus eight)) divide by 4) equally minus ( square root of (two) divide by two)
- cos*((pi(4x+48))/4)=-(√(2)/2)
- cos((pi(4x+48))/4)=-(sqrt(2)/2)
- cospi4x+48/4=-sqrt2/2
- cos*((pi(4x+48)) divide by 4)=-(sqrt(2) divide by 2)
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Similar expressions
- cospi(4x+132)/4=-sqrt(2)/2
- cos*((pi*(2*x+6))/4)=-(sqrt2/2)
- cos*((pi(4x+48))/4)=+(sqrt(2)/2)
- cos*((pi(4x-48))/4)=-(sqrt(2)/2)
- sinx/4=-sqrt2/2
- sin(-t/4)=-sqrt(2)/2
cos*((pi(4x+48))/4)=-(sqrt(2)/2) equation
The teacher will be very surprised to see your correct solution 😉
The solution
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[src]
___ /pi*(4*x + 48)\ -\/ 2 cos|-------------| = ------- \ 4 / 2
$$\cos{\left(\frac{\pi \left(4 x + 48\right)}{4} \right)} = - \frac{\sqrt{2}}{2}$$
Detail solution
Given the equation
$$\cos{\left(\frac{\pi \left(4 x + 48\right)}{4} \right)} = - \frac{\sqrt{2}}{2}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$\pi x = 2 \pi n + \operatorname{acos}{\left(- \frac{\sqrt{2}}{2} \right)}$$
$$\pi x = 2 \pi n - \pi + \operatorname{acos}{\left(- \frac{\sqrt{2}}{2} \right)}$$
Or
$$\pi x = 2 \pi n + \frac{3 \pi}{4}$$
$$\pi x = 2 \pi n - \frac{\pi}{4}$$
, where n - is a integer
Divide both parts of the equation by
$$\pi$$
we get the answer:
$$x_{1} = \frac{2 \pi n + \frac{3 \pi}{4}}{\pi}$$
$$x_{2} = \frac{2 \pi n - \frac{\pi}{4}}{\pi}$$
$$\cos{\left(\frac{\pi \left(4 x + 48\right)}{4} \right)} = - \frac{\sqrt{2}}{2}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$\pi x = 2 \pi n + \operatorname{acos}{\left(- \frac{\sqrt{2}}{2} \right)}$$
$$\pi x = 2 \pi n - \pi + \operatorname{acos}{\left(- \frac{\sqrt{2}}{2} \right)}$$
Or
$$\pi x = 2 \pi n + \frac{3 \pi}{4}$$
$$\pi x = 2 \pi n - \frac{\pi}{4}$$
, where n - is a integer
Divide both parts of the equation by
$$\pi$$
we get the answer:
$$x_{1} = \frac{2 \pi n + \frac{3 \pi}{4}}{\pi}$$
$$x_{2} = \frac{2 \pi n - \frac{\pi}{4}}{\pi}$$
Sum and product of roots
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sum
3/4 + 5/4
$$\left(\frac{3}{4}\right) + \left(\frac{5}{4}\right)$$
=
2
$$2$$
product
3/4 * 5/4
$$\left(\frac{3}{4}\right) * \left(\frac{5}{4}\right)$$
=
15 -- 16
$$\frac{15}{16}$$
Numerical answer
[src]
x1 = -87.25
x2 = 60.75
x3 = -65.25
x4 = -55.25
x5 = 66.75
x6 = -33.25
x7 = 62.75
x8 = -97.25
x9 = 78.75
x10 = -91.25
x11 = 50.75
x12 = -43.25
x13 = 100.75
x14 = -63.25
x15 = 64.75
x16 = 98.75
x17 = -31.25
x18 = -81.25
x19 = -41.25
x20 = -69.25
x21 = 52.75
x22 = 20.75
x23 = 42.75
x24 = 40.75
x25 = 48.75
x26 = 28.75
x27 = -71.25
x28 = 94.75
x29 = -21.25
x30 = -95.25
x31 = -45.25
x32 = 26.75
x33 = 0.75
x34 = 82.75
x35 = -89.25
x36 = -49.25
x37 = -17.25
x38 = -99.25
x39 = 34.75
x40 = 46.75
x41 = 32.75
x42 = -37.25
x43 = -1.25
x44 = -27.25
x45 = -67.25
x46 = 8.75
x47 = -29.25
x48 = 4.75
x49 = -59.25
x50 = 12.75
x51 = -77.25
x52 = -79.25
x53 = 30.75
x54 = 96.75
x55 = 44.75
x56 = -51.25
x57 = -9.25
x58 = -19.25
x59 = 6.75
x60 = 16.75
x61 = -15.25
x62 = -35.25
x63 = 58.75
x64 = -3.25
x65 = 70.75
x66 = -13.25
x67 = -47.25
x68 = -73.25
x69 = 10.75
x70 = -61.25
x71 = 84.75
x72 = 72.75
x73 = -11.25
x74 = -5.25
x75 = 18.75
x76 = -83.25
x77 = 74.75
x78 = -57.25
x79 = 68.75
x80 = -93.25
x81 = 24.75
x82 = -23.25
x83 = -7.25
x84 = -39.25
x85 = 86.75
x86 = 56.75
x87 = 92.75
x88 = -85.25
x89 = 76.75
x90 = 88.75
x91 = 22.75
x92 = 36.75
x93 = 90.75
x94 = -25.25
x95 = -75.25
x96 = 14.75
x97 = 80.75
x98 = 38.75
x99 = 54.75
x100 = 2.75
x101 = -53.25
x101 = -53.25
The graph