Mister Exam
Other calculators
-
How to use it?
- Equation:
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Equation cos(x)=3/4
- Equation x^2-4x-45=0
-
Equation (x^2-9)^2+(x^2-2*x-15)^2=0
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Equation sqrt(x^3-4*x^2-10*x+29)=3-x
- Express {x} in terms of y where:
- 4*x+15*y=19
- -19*x-14*y=-8
- -14*x-3*y=-5
- -8*x-12*y=15
- Derivative of:
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cos(x)
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3/4
- Graphing y =:
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cos(x)
- Integral of d{x}:
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cos(x)
- Sum of series:
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3/4
- Limit of the function:
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3/4
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Identical expressions
- cos(x)= three / four
- co sinus of e of (x) equally 3 divide by 4
- co sinus of e of (x) equally three divide by four
- cosx=3/4
- cos(x)=3 divide by 4
-
Similar expressions
- 3sin^2x-7sinx×cosx+2cos^2x=0
- cosx+sinx=sqrt2*sin(2x)
- (x+3)/12-1*(x-3)/4=(x+2)/6
- cosx=3/4
cos(x)=3/4 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$\cos{\left(x \right)} = \frac{3}{4}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$x = \pi n + \operatorname{acos}{\left(\frac{3}{4} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(\frac{3}{4} \right)}$$
Or
$$x = \pi n + \operatorname{acos}{\left(\frac{3}{4} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(\frac{3}{4} \right)}$$
, where n - is a integer
$$\cos{\left(x \right)} = \frac{3}{4}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$x = \pi n + \operatorname{acos}{\left(\frac{3}{4} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(\frac{3}{4} \right)}$$
Or
$$x = \pi n + \operatorname{acos}{\left(\frac{3}{4} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(\frac{3}{4} \right)}$$
, where n - is a integer
Sum and product of roots
[src]
sum
-acos(3/4) + 2*pi + acos(3/4)
$$\operatorname{acos}{\left(\frac{3}{4} \right)} + \left(- \operatorname{acos}{\left(\frac{3}{4} \right)} + 2 \pi\right)$$
=
2*pi
$$2 \pi$$
product
(-acos(3/4) + 2*pi)*acos(3/4)
$$\left(- \operatorname{acos}{\left(\frac{3}{4} \right)} + 2 \pi\right) \operatorname{acos}{\left(\frac{3}{4} \right)}$$
=
(-acos(3/4) + 2*pi)*acos(3/4)
$$\left(- \operatorname{acos}{\left(\frac{3}{4} \right)} + 2 \pi\right) \operatorname{acos}{\left(\frac{3}{4} \right)}$$
(-acos(3/4) + 2*pi)*acos(3/4)
Rapid solution
[src]
x1 = -acos(3/4) + 2*pi
$$x_{1} = - \operatorname{acos}{\left(\frac{3}{4} \right)} + 2 \pi$$
x2 = acos(3/4)
$$x_{2} = \operatorname{acos}{\left(\frac{3}{4} \right)}$$
x2 = acos(3/4)
Numerical answer
[src]
x1 = 7.005919554993
x2 = 32.1386607837113
x3 = 99.80823066706
x4 = 13.2891048621726
x5 = -94.9705138555072
x6 = -49.5427482096233
x7 = -68.392304131162
x8 = -80.9586747455212
x9 = -57.2714020124297
x10 = 63.5545873196093
x11 = 69.8377726267889
x12 = -55.8259335168029
x13 = 88.6873285483276
x14 = 18.1268216737253
x15 = 30.6931922880845
x16 = 157.802366927303
x17 = 36.9763775952641
x18 = 87.2418600527008
x19 = -24.4100069809049
x20 = -11.8436363665458
x21 = 94.9705138555072
x22 = 76.1209579339685
x23 = -87.2418600527008
x24 = -44.7050313980705
x25 = 82.404143241148
x26 = 74.6754894383416
x27 = -19.5722901693522
x28 = 93.5250453598804
x29 = 25.8554754765318
x30 = -69.8377726267889
x31 = -32.1386607837113
x32 = 24.4100069809049
x33 = 16770.5443191101
x34 = -0.722734247813416
x35 = 5.56045105936617
x36 = 420.250681333219
x37 = 0.722734247813416
x38 = -25.8554754765318
x39 = -93.5250453598804
x40 = 44.7050313980705
x41 = -76.1209579339685
x42 = 80.9586747455212
x43 = -99.80823066706
x44 = 62.1091188239824
x45 = -36.9763775952641
x46 = -62.1091188239824
x47 = -38.4218460908909
x48 = -13.2891048621726
x49 = 38.4218460908909
x50 = -30.6931922880845
x51 = -5.56045105936617
x52 = 57.2714020124297
x53 = 50.9882167052501
x54 = 43.2595629024437
x55 = 68.392304131162
x56 = 19.5722901693522
x57 = -88.6873285483276
x58 = 11.8436363665458
x59 = -43.2595629024437
x60 = -18.1268216737253
x61 = 49.5427482096233
x62 = 55.8259335168029
x63 = -101.253699162687
x64 = -74.6754894383416
x65 = -82.404143241148
x66 = -50.9882167052501
x67 = -7.005919554993
x68 = -63.5545873196093
x68 = -63.5545873196093
The graph