Mister Exam
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How to use it?
- Equation:
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- Equation x:2,404=5,02
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Equation tgx/3=sqrt(3)/3
- Equation 4+(2x-(4x-1))+x=-5-x
- Express {x} in terms of y where:
- -1*x-19*y=-10
- 5*x+5*y=20
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- Limit of the function:
-
sqrt(2)/2
- sqrt(2)/2
-
Identical expressions
- cos((pi*(x+ one))/ four)=sqrt(two)/ two
- co sinus of e of (( Pi multiply by (x plus 1)) divide by 4) equally square root of (2) divide by 2
- co sinus of e of (( Pi multiply by (x plus one)) divide by four) equally square root of (two) divide by two
- cos((pi*(x+1))/4)=√(2)/2
- cos((pi(x+1))/4)=sqrt(2)/2
- cospix+1/4=sqrt2/2
- cos((pi*(x+1)) divide by 4)=sqrt(2) divide by 2
-
Similar expressions
- cos(pi*(x+1)/4)=√2/2
- cos(pi*(x+1)/4)=2^(1/2)/2
- cos*pi*(x+1)/4=sqrt(2)/2
- sin(pi(x-3))/4=sqrt2/2
- cospi(x+1)/4=√2/2
- cos((pi*(x-1))/4)=sqrt(2)/2
cos((pi*(x+1))/4)=sqrt(2)/2 equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
___ /pi*(x + 1)\ \/ 2 cos|----------| = ----- \ 4 / 2
$$\cos{\left(\frac{\pi \left(x + 1\right)}{4} \right)} = \frac{\sqrt{2}}{2}$$
Detail solution
Given the equation
$$\cos{\left(\frac{\pi \left(x + 1\right)}{4} \right)} = \frac{\sqrt{2}}{2}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$\frac{\pi x}{4} + \frac{\pi}{4} = 2 \pi n + \operatorname{acos}{\left(\frac{\sqrt{2}}{2} \right)}$$
$$\frac{\pi x}{4} + \frac{\pi}{4} = 2 \pi n - \pi + \operatorname{acos}{\left(\frac{\sqrt{2}}{2} \right)}$$
Or
$$\frac{\pi x}{4} + \frac{\pi}{4} = 2 \pi n + \frac{\pi}{4}$$
$$\frac{\pi x}{4} + \frac{\pi}{4} = 2 \pi n - \frac{3 \pi}{4}$$
, where n - is a integer
Move
$$\frac{\pi}{4}$$
to right part of the equation with the opposite sign, in total:
$$\frac{\pi x}{4} = 2 \pi n$$
$$\frac{\pi x}{4} = 2 \pi n - \pi$$
Divide both parts of the equation by
$$\frac{\pi}{4}$$
we get the answer:
$$x_{1} = 8 n$$
$$x_{2} = \frac{4 \cdot \left(2 \pi n - \pi\right)}{\pi}$$
$$\cos{\left(\frac{\pi \left(x + 1\right)}{4} \right)} = \frac{\sqrt{2}}{2}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$\frac{\pi x}{4} + \frac{\pi}{4} = 2 \pi n + \operatorname{acos}{\left(\frac{\sqrt{2}}{2} \right)}$$
$$\frac{\pi x}{4} + \frac{\pi}{4} = 2 \pi n - \pi + \operatorname{acos}{\left(\frac{\sqrt{2}}{2} \right)}$$
Or
$$\frac{\pi x}{4} + \frac{\pi}{4} = 2 \pi n + \frac{\pi}{4}$$
$$\frac{\pi x}{4} + \frac{\pi}{4} = 2 \pi n - \frac{3 \pi}{4}$$
, where n - is a integer
Move
$$\frac{\pi}{4}$$
to right part of the equation with the opposite sign, in total:
$$\frac{\pi x}{4} = 2 \pi n$$
$$\frac{\pi x}{4} = 2 \pi n - \pi$$
Divide both parts of the equation by
$$\frac{\pi}{4}$$
we get the answer:
$$x_{1} = 8 n$$
$$x_{2} = \frac{4 \cdot \left(2 \pi n - \pi\right)}{\pi}$$
Sum and product of roots
[src]
sum
0 + 6
$$\left(0\right) + \left(6\right)$$
=
6
$$6$$
product
0 * 6
$$\left(0\right) * \left(6\right)$$
=
0
$$0$$
Numerical answer
[src]
x1 = 0.0
x2 = -88.0
x3 = 94.0
x4 = 6.0
x5 = 24.0
x6 = 38.0
x7 = 48.0
x8 = -90.0
x9 = -10.0
x10 = -16.0
x11 = -26.0
x12 = 32.0
x13 = -42.0
x14 = 54.0
x15 = 78.0
x16 = -40.0
x17 = 102.0
x18 = -64.0
x19 = 72.0
x20 = 30.0
x21 = 56.0
x22 = -58.0
x23 = -56.0
x24 = -66.0
x25 = -2.0
x26 = 62.0
x27 = -82.0
x28 = -80.0
x29 = -32.0
x30 = -24.0
x31 = -98.0
x32 = 16.0
x33 = 8.0
x34 = -48.0
x35 = 80.0
x36 = 40.0
x37 = -74.0
x38 = -34.0
x39 = -8.0
x40 = 86.0
x41 = 96.0
x42 = -50.0
x43 = 88.0
x44 = 46.0
x45 = 22.0
x46 = -72.0
x47 = -18.0
x48 = 14.0
x49 = 70.0
x50 = -96.0
x51 = 64.0
x51 = 64.0
The graph