Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation cos(x)=-3
-
Equation (x+3)^3=81*(x+3)
-
Equation x^4=(3x-10)^2
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Equation 4^x+3=11^x
- Express {x} in terms of y where:
- -20*x+5*y=13
- 9*x+9*y=18
- -11*x-16*y=-19
- 3*x-3*y=-14
- Graphing y =:
- cos(x/2)
- Derivative of:
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cos(x/2)
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sqrt(3)/2
- Limit of the function:
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cos(x/2)
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sqrt(3)/2
-
Identical expressions
- cos(x/ two)=sqrt(three)/ two
- co sinus of e of (x divide by 2) equally square root of (3) divide by 2
- co sinus of e of (x divide by two) equally square root of (three) divide by two
- cos(x/2)=√(3)/2
- cosx/2=sqrt3/2
- cos(x divide by 2)=sqrt(3) divide by 2
-
Similar expressions
- -17cos(x)/2+17/2=0
- cos(x/2-п/7)=√3/2
- cosx/2+1=0
cos(x/2)=sqrt(3)/2 equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
___ /x\ \/ 3 cos|-| = ----- \2/ 2
$$\cos{\left(\frac{x}{2} \right)} = \frac{\sqrt{3}}{2}$$
Detail solution
Given the equation
$$\cos{\left(\frac{x}{2} \right)} = \frac{\sqrt{3}}{2}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$\frac{x}{2} = \pi n + \operatorname{acos}{\left(\frac{\sqrt{3}}{2} \right)}$$
$$\frac{x}{2} = \pi n - \pi + \operatorname{acos}{\left(\frac{\sqrt{3}}{2} \right)}$$
Or
$$\frac{x}{2} = \pi n + \frac{\pi}{6}$$
$$\frac{x}{2} = \pi n - \frac{5 \pi}{6}$$
, where n - is a integer
Divide both parts of the equation by
$$\frac{1}{2}$$
we get the answer:
$$x_{1} = 2 \pi n + \frac{\pi}{3}$$
$$x_{2} = 2 \pi n - \frac{5 \pi}{3}$$
$$\cos{\left(\frac{x}{2} \right)} = \frac{\sqrt{3}}{2}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$\frac{x}{2} = \pi n + \operatorname{acos}{\left(\frac{\sqrt{3}}{2} \right)}$$
$$\frac{x}{2} = \pi n - \pi + \operatorname{acos}{\left(\frac{\sqrt{3}}{2} \right)}$$
Or
$$\frac{x}{2} = \pi n + \frac{\pi}{6}$$
$$\frac{x}{2} = \pi n - \frac{5 \pi}{6}$$
, where n - is a integer
Divide both parts of the equation by
$$\frac{1}{2}$$
we get the answer:
$$x_{1} = 2 \pi n + \frac{\pi}{3}$$
$$x_{2} = 2 \pi n - \frac{5 \pi}{3}$$
Rapid solution
[src]
pi
x1 = --
3
$$x_{1} = \frac{\pi}{3}$$
11*pi
x2 = -----
3
$$x_{2} = \frac{11 \pi}{3}$$
x2 = 11*pi/3
Sum and product of roots
[src]
sum
pi 11*pi -- + ----- 3 3
$$\frac{\pi}{3} + \frac{11 \pi}{3}$$
=
4*pi
$$4 \pi$$
product
pi 11*pi --*----- 3 3
$$\frac{\pi}{3} \frac{11 \pi}{3}$$
=
2 11*pi ------ 9
$$\frac{11 \pi^{2}}{9}$$
11*pi^2/9
Numerical answer
[src]
x1 = 1.0471975511966
x2 = 13.6135681655558
x3 = -86.9173967493176
x4 = 99.4837673636768
x5 = 86.9173967493176
x6 = -99.4837673636768
x7 = 36.6519142918809
x8 = -13.6135681655558
x9 = 51.3126800086333
x10 = -36.6519142918809
x11 = -76.4454212373516
x12 = -89.0117918517108
x13 = 49.2182849062401
x14 = -49.2182849062401
x15 = 38.7463093942741
x16 = 63.8790506229925
x17 = -11.5191730631626
x18 = 26.1799387799149
x19 = -164.410015537866
x20 = -225.147473507269
x21 = 74.3510261349584
x22 = -24.0855436775217
x23 = -2286.03225426217
x24 = -12881.5770772693
x25 = -61.7846555205993
x26 = 24.0855436775217
x27 = 61.7846555205993
x28 = 11.5191730631626
x29 = -74.3510261349584
x30 = -63.8790506229925
x31 = -26.1799387799149
x32 = 89.0117918517108
x33 = -1.0471975511966
x34 = 76.4454212373516
x35 = 137.182879206754
x36 = -38.7463093942741
x37 = -51.3126800086333
x37 = -51.3126800086333
The graph