Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation cos(x)=1/8
-
Equation (2*x-6)^2-4*x^2=0
-
Equation 12-y+2=0
-
Equation x^3+9*x^2+27*x+27=0
- Express {x} in terms of y where:
- -20*x+6*y=-12
- 12*x-2*y=-18
- -16*x-19*y=-4
- -20*x-8*y=3
- Derivative of:
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cos(x)
- 1/8
- Graphing y =:
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cos(x)
- Integral of d{x}:
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cos(x)
- 1/8
- Sum of series:
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1/8
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Identical expressions
- cos(x)= one / eight
- co sinus of e of (x) equally 1 divide by 8
- co sinus of e of (x) equally one divide by eight
- cosx=1/8
- cos(x)=1 divide by 8
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Similar expressions
- 2sin^2x-5sinxcosx-cos^2x=2
- 30*(sinx-0.125*cosx)=10.9
- cosx=1/8
cos(x)=1/8 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$\cos{\left(x \right)} = \frac{1}{8}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$x = \pi n + \operatorname{acos}{\left(\frac{1}{8} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(\frac{1}{8} \right)}$$
Or
$$x = \pi n + \operatorname{acos}{\left(\frac{1}{8} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(\frac{1}{8} \right)}$$
, where n - is a integer
$$\cos{\left(x \right)} = \frac{1}{8}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$x = \pi n + \operatorname{acos}{\left(\frac{1}{8} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(\frac{1}{8} \right)}$$
Or
$$x = \pi n + \operatorname{acos}{\left(\frac{1}{8} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(\frac{1}{8} \right)}$$
, where n - is a integer
Rapid solution
[src]
x1 = -acos(1/8) + 2*pi
$$x_{1} = - \operatorname{acos}{\left(\frac{1}{8} \right)} + 2 \pi$$
x2 = acos(1/8)
$$x_{2} = \operatorname{acos}{\left(\frac{1}{8} \right)}$$
x2 = acos(1/8)
Sum and product of roots
[src]
sum
-acos(1/8) + 2*pi + acos(1/8)
$$\operatorname{acos}{\left(\frac{1}{8} \right)} + \left(- \operatorname{acos}{\left(\frac{1}{8} \right)} + 2 \pi\right)$$
=
2*pi
$$2 \pi$$
product
(-acos(1/8) + 2*pi)*acos(1/8)
$$\left(- \operatorname{acos}{\left(\frac{1}{8} \right)} + 2 \pi\right) \operatorname{acos}{\left(\frac{1}{8} \right)}$$
=
(-acos(1/8) + 2*pi)*acos(1/8)
$$\left(- \operatorname{acos}{\left(\frac{1}{8} \right)} + 2 \pi\right) \operatorname{acos}{\left(\frac{1}{8} \right)}$$
(-acos(1/8) + 2*pi)*acos(1/8)
Numerical answer
[src]
x1 = -99.0854964192466
x2 = 64.2773215674227
x3 = -11.1209021187323
x4 = -42.5368286546303
x5 = -86.5191258048874
x6 = 45.4277656458839
x7 = 51.7109509530635
x8 = -45.4277656458839
x9 = -1490.56038629719
x10 = 70.5605068746023
x11 = 89.410062796141
x12 = 11.1209021187323
x13 = 83.1268774889615
x14 = 55.1031992689894
x15 = -1.44546849562683
x16 = 92.802311112067
x17 = -61.386384576169
x18 = 42.5368286546303
x19 = -29.9704580402711
x20 = -83.1268774889615
x21 = 29.9704580402711
x22 = -32.8613950315248
x23 = 57.9941362602431
x24 = -73.9527551905282
x25 = -23.6872727330915
x26 = -92.802311112067
x27 = -48.8200139618099
x28 = -14.011839109986
x29 = 39.1445803387044
x30 = 48.8200139618099
x31 = 76.8436921817819
x32 = -20.2950244171656
x33 = 1.44546849562683
x34 = -95.6932481033206
x35 = 99.0854964192466
x36 = -57.9941362602431
x37 = 26.5782097243452
x38 = 86.5191258048874
x39 = 7.72865380280642
x40 = -7.72865380280642
x41 = 73.9527551905282
x42 = 32.8613950315248
x43 = 20.2950244171656
x44 = -89.410062796141
x45 = 17.4040874259119
x46 = -4.83771681155276
x47 = -70.5605068746023
x48 = 14.011839109986
x49 = 36.2536433474507
x50 = -55.1031992689894
x51 = -76.8436921817819
x52 = 80.2359404977078
x53 = 67.6695698833486
x54 = 617.197628599226
x55 = -64.2773215674227
x56 = -17.4040874259119
x57 = -67.6695698833486
x58 = -51.7109509530635
x59 = -80.2359404977078
x60 = 23.6872727330915
x61 = 95.6932481033206
x62 = 61.386384576169
x63 = -39.1445803387044
x64 = 4.83771681155276
x65 = -36.2536433474507
x66 = -26.5782097243452
x66 = -26.5782097243452
The graph