Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation (x^2-1)/(x+2)=4x
-
Equation 3*x+5+(x+5)=(1-x)+4
-
Equation cos(x)=3/4
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Equation cos(x)=(1/2)
- Express {x} in terms of y where:
- 18*x-20*y=-7
- -13*x+7*y=11
- -19*x-14*y=-8
- 4*x+18*y=-14
- Derivative of:
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cos(x)
- (1/2)
- Integral of d{x}:
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cos(x)
- Graphing y =:
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cos(x)
- Sum of series:
-
(1/2)
-
Identical expressions
- cos(x)=(one / two)
- co sinus of e of (x) equally (1 divide by 2)
- co sinus of e of (x) equally (one divide by two)
- cosx=1/2
- cos(x)=(1 divide by 2)
-
Similar expressions
- r+1/(r+1/(r+2/r)+1/(2*r))+1/(3*r)=219
- -tan(x/2)=1/2*ln(2)
- cos4*pi*x/3=-1/2
- tg(x)=1/2
- 2sinx^2+1,5sin2x-3cos(x^2)=1
- cosx=(1/2)
cos(x)=(1/2) equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$\cos{\left(x \right)} = \frac{1}{2}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$x = \pi n + \operatorname{acos}{\left(\frac{1}{2} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(\frac{1}{2} \right)}$$
Or
$$x = \pi n + \frac{\pi}{3}$$
$$x = \pi n - \frac{2 \pi}{3}$$
, where n - is a integer
$$\cos{\left(x \right)} = \frac{1}{2}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$x = \pi n + \operatorname{acos}{\left(\frac{1}{2} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(\frac{1}{2} \right)}$$
Or
$$x = \pi n + \frac{\pi}{3}$$
$$x = \pi n - \frac{2 \pi}{3}$$
, where n - is a integer
Rapid solution
[src]
pi
x1 = --
3
$$x_{1} = \frac{\pi}{3}$$
5*pi
x2 = ----
3
$$x_{2} = \frac{5 \pi}{3}$$
x2 = 5*pi/3
Sum and product of roots
[src]
sum
pi 5*pi -- + ---- 3 3
$$\frac{\pi}{3} + \frac{5 \pi}{3}$$
=
2*pi
$$2 \pi$$
product
pi 5*pi --*---- 3 3
$$\frac{\pi}{3} \frac{5 \pi}{3}$$
=
2 5*pi ----- 9
$$\frac{5 \pi^{2}}{9}$$
5*pi^2/9
Numerical answer
[src]
x1 = 45.0294947014537
x2 = -17.8023583703422
x3 = 38.7463093942741
x4 = -32.4631240870945
x5 = 89.0117918517108
x6 = -63.8790506229925
x7 = -24.0855436775217
x8 = -86.9173967493176
x9 = -49.2182849062401
x10 = 49.2182849062401
x11 = 51.3126800086333
x12 = -82.7286065445312
x13 = 19.8967534727354
x14 = -99.4837673636768
x15 = 68.0678408277789
x16 = -13.6135681655558
x17 = 5.23598775598299
x18 = -26.1799387799149
x19 = -30.3687289847013
x20 = -74.3510261349584
x21 = -225.147473507269
x22 = -7.33038285837618
x23 = 63.8790506229925
x24 = 57.5958653158129
x25 = 74.3510261349584
x26 = 1651.43053823704
x27 = -93.2005820564972
x28 = -5.23598775598299
x29 = -76.4454212373516
x30 = 32.4631240870945
x31 = -45.0294947014537
x32 = -42.9350995990605
x33 = 30.3687289847013
x34 = 36.6519142918809
x35 = 26.1799387799149
x36 = -19.8967534727354
x37 = 55.5014702134197
x38 = 13.6135681655558
x39 = -57.5958653158129
x40 = 17.8023583703422
x41 = -36.6519142918809
x42 = -38.7463093942741
x43 = -51.3126800086333
x44 = 1.0471975511966
x45 = -68.0678408277789
x46 = 42.9350995990605
x47 = 61.7846555205993
x48 = -1.0471975511966
x49 = 70.162235930172
x50 = 99.4837673636768
x51 = 76.4454212373516
x52 = -359.188760060433
x53 = -70.162235930172
x54 = 95.2949771588904
x55 = -55.5014702134197
x56 = 82.7286065445312
x57 = -95.2949771588904
x58 = 7.33038285837618
x59 = -80.634211442138
x60 = 93.2005820564972
x61 = -11.5191730631626
x62 = 11.5191730631626
x63 = -61.7846555205993
x64 = 24.0855436775217
x65 = 86.9173967493176
x66 = 80.634211442138
x67 = -89.0117918517108
x67 = -89.0117918517108
The graph