Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation 8x-15=-12+5x
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Equation x^2-x-7=0
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Equation 141*10^(-6)*x*3*sqrt(2)=sqrt((1-19881*10^(-12)*x^2)^2+9)
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Equation x^3-6*x^2+x-6=0
- Express {x} in terms of y where:
- -20*x-4*y=-14
- 17*x+9*y=0
- -7*x+18*y=5
- -19*x-8*y=-12
- Derivative of:
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cos(x)
- Graphing y =:
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cos(x)
- Integral of d{x}:
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cos(x)
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Identical expressions
- cos(x)=(two / five)
- co sinus of e of (x) equally (2 divide by 5)
- co sinus of e of (x) equally (two divide by five)
- cosx=2/5
- cos(x)=(2 divide by 5)
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Similar expressions
- x/15-2/5=-2,3
- cosx=(2/5)
cos(x)=(2/5) equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$\cos{\left(x \right)} = \frac{2}{5}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$x = \pi n + \operatorname{acos}{\left(\frac{2}{5} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(\frac{2}{5} \right)}$$
Or
$$x = \pi n + \operatorname{acos}{\left(\frac{2}{5} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(\frac{2}{5} \right)}$$
, where n - is a integer
$$\cos{\left(x \right)} = \frac{2}{5}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$x = \pi n + \operatorname{acos}{\left(\frac{2}{5} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(\frac{2}{5} \right)}$$
Or
$$x = \pi n + \operatorname{acos}{\left(\frac{2}{5} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(\frac{2}{5} \right)}$$
, where n - is a integer
Sum and product of roots
[src]
sum
-acos(2/5) + 2*pi + acos(2/5)
$$\operatorname{acos}{\left(\frac{2}{5} \right)} + \left(- \operatorname{acos}{\left(\frac{2}{5} \right)} + 2 \pi\right)$$
=
2*pi
$$2 \pi$$
product
(-acos(2/5) + 2*pi)*acos(2/5)
$$\left(- \operatorname{acos}{\left(\frac{2}{5} \right)} + 2 \pi\right) \operatorname{acos}{\left(\frac{2}{5} \right)}$$
=
(-acos(2/5) + 2*pi)*acos(2/5)
$$\left(- \operatorname{acos}{\left(\frac{2}{5} \right)} + 2 \pi\right) \operatorname{acos}{\left(\frac{2}{5} \right)}$$
(-acos(2/5) + 2*pi)*acos(2/5)
Rapid solution
[src]
x1 = -acos(2/5) + 2*pi
$$x_{1} = - \operatorname{acos}{\left(\frac{2}{5} \right)} + 2 \pi$$
x2 = acos(2/5)
$$x_{2} = \operatorname{acos}{\left(\frac{2}{5} \right)}$$
x2 = acos(2/5)
Numerical answer
[src]
x1 = -93.0885001269664
x2 = -76.5575031668824
x3 = -67.955758898248
x4 = 80.5221295126072
x5 = 70.2743178597029
x6 = -57.7079472453437
x7 = -95.4070590884212
x8 = 86.8053148197868
x9 = 7.44246478790699
x10 = -82.840688474062
x11 = 6070.71628621621
x12 = -61.6725735910685
x13 = 36.5398323623501
x14 = -26.2920207094458
x15 = 89.1238737812416
x16 = 99.371685434146
x17 = 61.6725735910685
x18 = 30.2566470551705
x19 = -42.8230176695297
x20 = 5.12390582645218
x21 = 1.15927948072741
x22 = -20.0088354022662
x23 = -1.15927948072741
x24 = -5.12390582645218
x25 = -30.2566470551705
x26 = -17.6902764408113
x27 = -51.4247619381641
x28 = -23.9734617479909
x29 = 63.9911325525233
x30 = 38.8583913238049
x31 = -36.5398323623501
x32 = -70.2743178597029
x33 = 55.3893882838889
x34 = -49.1062029767093
x35 = -32.5752060166253
x36 = 143.353982584403
x37 = 20.0088354022662
x38 = 42.8230176695297
x39 = 45.1415766309845
x40 = 82.840688474062
x41 = 11.4070911336318
x42 = -80.5221295126072
x43 = 17.6902764408113
x44 = 32.5752060166253
x45 = 57.7079472453437
x46 = 95.4070590884212
x47 = -38.8583913238049
x48 = -74.2389442054276
x49 = -55.3893882838889
x50 = 51.4247619381641
x51 = -89.1238737812416
x52 = 93.0885001269664
x53 = 74.2389442054276
x54 = -99.371685434146
x55 = -86.8053148197868
x56 = -7.44246478790699
x57 = 67.955758898248
x58 = -13.7256500950866
x59 = 49.1062029767093
x60 = 13.7256500950866
x61 = 76.5575031668824
x62 = -63.9911325525233
x63 = -45.1415766309845
x64 = 23.9734617479909
x65 = 26.2920207094458
x66 = -11.4070911336318
x66 = -11.4070911336318
The graph