Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation 5^x=8^x
-
Equation -27x+220=-5x
-
Equation x+12=5
-
Equation 3/(x-5)+8/x=2
- Express {x} in terms of y where:
- 12*x+1*y=15
- -16*x-10*y=4
- -4*x-20*y=10
- 19*x+6*y=8
- Derivative of:
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cos
- Integral of d{x}:
-
cos
- cos
-
Identical expressions
- cos=-√ two / two
- co sinus of e of equally minus √2 divide by 2
- co sinus of e of equally minus √ two divide by two
- cos=-√2 divide by 2
-
Similar expressions
- (4x^4-(√2/2)x^2+1)(4x^4+(√2/2)x^2+1)=0
- cos=+√2/2
cos=-√2/2 equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
___
-\/ 2
cos(x) = -------
2
$$\cos{\left(x \right)} = \frac{\left(-1\right) \sqrt{2}}{2}$$
Detail solution
Given the equation
$$\cos{\left(x \right)} = \frac{\left(-1\right) \sqrt{2}}{2}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$x = \pi n + \operatorname{acos}{\left(- \frac{\sqrt{2}}{2} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(- \frac{\sqrt{2}}{2} \right)}$$
Or
$$x = \pi n + \frac{3 \pi}{4}$$
$$x = \pi n - \frac{\pi}{4}$$
, where n - is a integer
$$\cos{\left(x \right)} = \frac{\left(-1\right) \sqrt{2}}{2}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$x = \pi n + \operatorname{acos}{\left(- \frac{\sqrt{2}}{2} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(- \frac{\sqrt{2}}{2} \right)}$$
Or
$$x = \pi n + \frac{3 \pi}{4}$$
$$x = \pi n - \frac{\pi}{4}$$
, where n - is a integer
Rapid solution
[src]
3*pi
x1 = ----
4
$$x_{1} = \frac{3 \pi}{4}$$
5*pi
x2 = ----
4
$$x_{2} = \frac{5 \pi}{4}$$
x2 = 5*pi/4
Sum and product of roots
[src]
sum
3*pi 5*pi ---- + ---- 4 4
$$\frac{3 \pi}{4} + \frac{5 \pi}{4}$$
=
2*pi
$$2 \pi$$
product
3*pi 5*pi ----*---- 4 4
$$\frac{3 \pi}{4} \frac{5 \pi}{4}$$
=
2 15*pi ------ 16
$$\frac{15 \pi^{2}}{16}$$
15*pi^2/16
Numerical answer
[src]
x1 = 21.2057504117311
x2 = -65.1880475619882
x3 = -35.3429173528852
x4 = 47.9092879672443
x5 = 2.35619449019234
x6 = -98.174770424681
x7 = -3.92699081698724
x8 = -8.63937979737193
x9 = -79.3252145031423
x10 = -40.0553063332699
x11 = 3.92699081698724
x12 = 90.3207887907066
x13 = 29.0597320457056
x14 = 46.3384916404494
x15 = -33.7721210260903
x16 = 40.0553063332699
x17 = 52.621676947629
x18 = 104.457955731861
x19 = -58.9048622548086
x20 = -66.7588438887831
x21 = 98.174770424681
x22 = 65.1880475619882
x23 = -335.36501577071
x24 = -16.4933614313464
x25 = 8.63937979737193
x26 = 35.3429173528852
x27 = 58.9048622548086
x28 = -47.9092879672443
x29 = -10.2101761241668
x30 = 85.6083998103219
x31 = 33.7721210260903
x32 = -27.4889357189107
x33 = 96.6039740978861
x34 = 27.4889357189107
x35 = 54.1924732744239
x36 = -84.037603483527
x37 = -73.0420291959627
x38 = 10.2101761241668
x39 = 2584.745355741
x40 = -41.6261026600648
x41 = 41.6261026600648
x42 = 79.3252145031423
x43 = -14.9225651045515
x44 = -91.8915851175014
x45 = -46.3384916404494
x46 = 84.037603483527
x47 = 71.4712328691678
x48 = 77.7544181763474
x49 = -96.6039740978861
x50 = 60.4756585816035
x51 = 14.9225651045515
x52 = 255.254403104171
x53 = -90.3207887907066
x54 = 22.776546738526
x55 = -60.4756585816035
x56 = 39349.2333843756
x57 = -2.35619449019234
x58 = -29.0597320457056
x59 = -71.4712328691678
x60 = -52.621676947629
x61 = 66.7588438887831
x62 = 91.8915851175014
x63 = -22.776546738526
x64 = -21.2057504117311
x65 = 73.0420291959627
x66 = 16.4933614313464
x67 = -77.7544181763474
x68 = -54.1924732744239
x69 = -85.6083998103219
x69 = -85.6083998103219