Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation cos(x)=sqrt(2)/2
-
Equation (7x+9)-(11x-7)=8
-
Equation x^3-5x^2-x+5=0
-
Equation x^2-x-20=0
- Express {x} in terms of y where:
- 9*x-18*y=6
- -1*x+19*y=-10
- 10*x+9*y=-4
- -12*x+3*y=-9
- Derivative of:
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cos(x)
- Integral of d{x}:
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cos(x)
- Graphing y =:
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cos(x)
- Limit of the function:
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sqrt(2)/2
- sqrt(2)/2
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Identical expressions
- cos(x)=sqrt(two)/ two
- co sinus of e of (x) equally square root of (2) divide by 2
- co sinus of e of (x) equally square root of (two) divide by two
- cos(x)=√(2)/2
- cosx=sqrt2/2
- cos(x)=sqrt(2) divide by 2
-
Similar expressions
- cos(x)+sqrt((2-sqrt2)/2)*(sin(x)+1)=0
- 5cosx+sin4x−10x=x3+5
- sinx/4=-sqrt2/2
- sinx/1+cosx=1-cosx
- cos*((pi*(2*x+6))/4)=-(sqrt2/2)
- cosx=sqrt(2)/2
cos(x)=sqrt(2)/2 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$\cos{\left(x \right)} = \frac{\sqrt{2}}{2}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$x = 2 \pi n + \operatorname{acos}{\left(\frac{\sqrt{2}}{2} \right)}$$
$$x = 2 \pi n - \pi + \operatorname{acos}{\left(\frac{\sqrt{2}}{2} \right)}$$
Or
$$x = 2 \pi n + \frac{\pi}{4}$$
$$x = 2 \pi n - \frac{3 \pi}{4}$$
, where n - is a integer
$$\cos{\left(x \right)} = \frac{\sqrt{2}}{2}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$x = 2 \pi n + \operatorname{acos}{\left(\frac{\sqrt{2}}{2} \right)}$$
$$x = 2 \pi n - \pi + \operatorname{acos}{\left(\frac{\sqrt{2}}{2} \right)}$$
Or
$$x = 2 \pi n + \frac{\pi}{4}$$
$$x = 2 \pi n - \frac{3 \pi}{4}$$
, where n - is a integer
Sum and product of roots
[src]
sum
pi 7*pi -- + ---- 4 4
$$\left(\frac{\pi}{4}\right) + \left(\frac{7 \pi}{4}\right)$$
=
2*pi
$$2 \pi$$
product
pi 7*pi -- * ---- 4 4
$$\left(\frac{\pi}{4}\right) * \left(\frac{7 \pi}{4}\right)$$
=
2 7*pi ----- 16
$$\frac{7 \pi^{2}}{16}$$
Rapid solution
[src]
pi
x_1 = --
4
$$x_{1} = \frac{\pi}{4}$$
7*pi
x_2 = ----
4
$$x_{2} = \frac{7 \pi}{4}$$
Numerical answer
[src]
x1 = 93.4623814442964
x2 = 30.6305283725005
x3 = 87.1791961371168
x4 = -24.3473430653209
x5 = -7.06858347057703
x6 = -51.0508806208341
x7 = -74.6128255227576
x8 = 80.8960108299372
x9 = -87.1791961371168
x10 = -101.316363078271
x11 = -95.0331777710912
x12 = -93.4623814442964
x13 = 43.1968989868597
x14 = -88.7499924639117
x15 = -36.9137136796801
x16 = 25.9181393921158
x17 = -44.7676953136546
x18 = -5.49778714378214
x19 = 0.785398163397448
x20 = 68.329640215578
x21 = -19.6349540849362
x22 = -13.3517687777566
x23 = -38.484510006475
x24 = 44.7676953136546
x25 = 32.2013246992954
x26 = -80.8960108299372
x27 = -43.1968989868597
x28 = -82.4668071567321
x29 = 51.0508806208341
x30 = -62.0464549083984
x31 = 57.3340659280137
x32 = 82.4668071567321
x33 = 19.6349540849362
x34 = 11.7809724509617
x35 = 55.7632696012188
x36 = -63.6172512351933
x37 = -30.6305283725005
x38 = 95.0331777710912
x39 = -49.4800842940392
x40 = -57.3340659280137
x41 = 88.7499924639117
x42 = 76.1836218495525
x43 = 99.7455667514759
x44 = 24.3473430653209
x45 = -182.997772071605
x46 = 7.06858347057703
x47 = 18.0641577581413
x48 = -55.7632696012188
x49 = -68.329640215578
x50 = 74.6128255227576
x51 = 49.4800842940392
x52 = -351.072979038659
x53 = 63.6172512351933
x54 = -76.1836218495525
x55 = -69.9004365423729
x56 = -0.785398163397448
x57 = 38.484510006475
x58 = -162.577419823272
x59 = 13.3517687777566
x60 = 36.9137136796801
x61 = 5.49778714378214
x62 = -99.7455667514759
x63 = -25.9181393921158
x64 = 62.0464549083984
x65 = -18.0641577581413
x66 = 69.9004365423729
x67 = -32.2013246992954
x68 = -11.7809724509617
x68 = -11.7809724509617
The graph