Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation cos(x)=√3/2
- Equation x^2-x-56=0
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Equation cos(x)=-1/4
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Equation |a|=9
- Express {x} in terms of y where:
- -19*x-4*y=5
- 19*x+3*y=-3
- 9*x+1*y=-18
- -2*x+7*y=4
- 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)
- Limit of the function:
- -1/4
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Identical expressions
- cos(x)=- one / four
- co sinus of e of (x) equally minus 1 divide by 4
- co sinus of e of (x) equally minus one divide by four
- cosx=-1/4
- cos(x)=-1 divide by 4
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Similar expressions
- 2cosx=1
- 4x^2*(-(1/4)x^3)=32
- cos(x)=+1/4
- 8^(n-2)((3/8)y^(n+2)-(1/4)y)
- cosx=-1/4
cos(x)=-1/4 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$\cos{\left(x \right)} = - \frac{1}{4}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$x = \pi n + \operatorname{acos}{\left(- \frac{1}{4} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(- \frac{1}{4} \right)}$$
Or
$$x = \pi n + \operatorname{acos}{\left(- \frac{1}{4} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(- \frac{1}{4} \right)}$$
, where n - is a integer
$$\cos{\left(x \right)} = - \frac{1}{4}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$x = \pi n + \operatorname{acos}{\left(- \frac{1}{4} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(- \frac{1}{4} \right)}$$
Or
$$x = \pi n + \operatorname{acos}{\left(- \frac{1}{4} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(- \frac{1}{4} \right)}$$
, where n - is a integer
Rapid solution
[src]
x1 = -acos(-1/4) + 2*pi
$$x_{1} = - \operatorname{acos}{\left(- \frac{1}{4} \right)} + 2 \pi$$
x2 = acos(-1/4)
$$x_{2} = \operatorname{acos}{\left(- \frac{1}{4} \right)}$$
x2 = acos(-1/4)
Sum and product of roots
[src]
sum
-acos(-1/4) + 2*pi + acos(-1/4)
$$\operatorname{acos}{\left(- \frac{1}{4} \right)} + \left(- \operatorname{acos}{\left(- \frac{1}{4} \right)} + 2 \pi\right)$$
=
2*pi
$$2 \pi$$
product
(-acos(-1/4) + 2*pi)*acos(-1/4)
$$\left(- \operatorname{acos}{\left(- \frac{1}{4} \right)} + 2 \pi\right) \operatorname{acos}{\left(- \frac{1}{4} \right)}$$
=
(-acos(-1/4) + 2*pi)*acos(-1/4)
$$\left(- \operatorname{acos}{\left(- \frac{1}{4} \right)} + 2 \pi\right) \operatorname{acos}{\left(- \frac{1}{4} \right)}$$
(-acos(-1/4) + 2*pi)*acos(-1/4)
Numerical answer
[src]
x1 = -23.3092646467814
x2 = 45.8057737321941
x3 = -79.8579324113977
x4 = -67.2915617970385
x5 = 89.7880708824512
x6 = -77.221700268092
x7 = -52.0889590393737
x8 = -20.6730325034757
x9 = -8.10666188911656
x10 = 67.2915617970385
x11 = -45.8057737321941
x12 = -35.8756352611405
x13 = 26.9562178106553
x14 = 98.7074883329364
x15 = -17.0260793396018
x16 = -4.45970872524261
x17 = 1.82347658193698
x18 = 92.4243030257568
x19 = 54.7251911826793
x20 = 61.0083764898589
x21 = 8.10666188911656
x22 = 33.2394031178349
x23 = 20.6730325034757
x24 = -83.5048855752716
x25 = 17.0260793396018
x26 = 52.0889590393737
x27 = -64.6553296537328
x28 = 79.8579324113977
x29 = -73.5747471042181
x30 = -42.1588205683201
x31 = -98.7074883329364
x32 = 4.45970872524261
x33 = 70.9385149609124
x34 = 42.1588205683201
x35 = -89.7880708824512
x36 = -14.3898471962961
x37 = -39.5225884250145
x38 = 64.6553296537328
x39 = 39.5225884250145
x40 = 58.3721443465533
x41 = -54.7251911826793
x42 = 83.5048855752716
x43 = -61.0083764898589
x44 = 77.221700268092
x45 = -96.0712561896308
x46 = 73.5747471042181
x47 = -48.4420058754997
x48 = -86.1411177185772
x49 = 23.3092646467814
x50 = 29.592449953961
x51 = -10.7428940324222
x52 = 86.1411177185772
x53 = 35.8756352611405
x54 = -58.3721443465533
x55 = -92.4243030257568
x56 = 14.3898471962961
x57 = -29.592449953961
x58 = -1.82347658193698
x59 = 96.0712561896308
x60 = 10.7428940324222
x61 = -26.9562178106553
x62 = 48.4420058754997
x63 = -33.2394031178349
x64 = -70.9385149609124
x64 = -70.9385149609124
The graph