Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation x^3+4*x^2-x-4=0
-
Equation cos(x)=3
-
Equation x^4+x^2-20=0
-
Equation cos(x/2)=0
- Express {x} in terms of y where:
- 16*x-17*y=-9
- 20*x+13*y=1
- -19*x+1*y=0
- 9*x+17*y=13
- Graphing y =:
- cos(x/2)
- Derivative of:
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cos(x/2)
- Limit of the function:
-
cos(x/2)
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Identical expressions
- cos(x/ two)= zero
- co sinus of e of (x divide by 2) equally 0
- co sinus of e of (x divide by two) equally zero
- cosx/2=0
- cos(x/2)=O
- cos(x divide by 2)=0
-
Similar expressions
- cos(x/2-Pi/8)=0
- cos(x/2-pi/6)=1
cos(x/2)=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$\cos{\left(\frac{x}{2} \right)} = 0$$
- this is the simplest trigonometric equation
We get:
$$\cos{\left(\frac{x}{2} \right)} = 0$$
This equation is transformed to
$$\frac{x}{2} = \pi n + \operatorname{acos}{\left(0 \right)}$$
$$\frac{x}{2} = \pi n - \pi + \operatorname{acos}{\left(0 \right)}$$
Or
$$\frac{x}{2} = \pi n + \frac{\pi}{2}$$
$$\frac{x}{2} = \pi n - \frac{\pi}{2}$$
, where n - is a integer
Divide both parts of the equation by
$$\frac{1}{2}$$
we get the answer:
$$x_{1} = 2 \pi n + \pi$$
$$x_{2} = 2 \pi n - \pi$$
$$\cos{\left(\frac{x}{2} \right)} = 0$$
- this is the simplest trigonometric equation
with the change of sign in 0
We get:
$$\cos{\left(\frac{x}{2} \right)} = 0$$
This equation is transformed to
$$\frac{x}{2} = \pi n + \operatorname{acos}{\left(0 \right)}$$
$$\frac{x}{2} = \pi n - \pi + \operatorname{acos}{\left(0 \right)}$$
Or
$$\frac{x}{2} = \pi n + \frac{\pi}{2}$$
$$\frac{x}{2} = \pi n - \frac{\pi}{2}$$
, where n - is a integer
Divide both parts of the equation by
$$\frac{1}{2}$$
we get the answer:
$$x_{1} = 2 \pi n + \pi$$
$$x_{2} = 2 \pi n - \pi$$
Sum and product of roots
[src]
sum
pi + 3*pi
$$\pi + 3 \pi$$
=
4*pi
$$4 \pi$$
product
pi*3*pi
$$\pi 3 \pi$$
=
2 3*pi
$$3 \pi^{2}$$
3*pi^2
Numerical answer
[src]
x1 = -97.3893722612836
x2 = 72.2566310325652
x3 = -40.8407044966673
x4 = -78.5398163397448
x5 = -3.14159265358979
x6 = 34.5575191894877
x7 = 84.8230016469244
x8 = -34.5575191894877
x9 = 9.42477796076938
x10 = 65.9734457253857
x11 = 40.8407044966673
x12 = -53.4070751110265
x13 = -84.8230016469244
x14 = -15.707963267949
x15 = -9.42477796076938
x16 = 15.707963267949
x17 = 28.2743338823081
x18 = 21.9911485751286
x19 = -47.1238898038469
x20 = -91.106186954104
x21 = 3.14159265358979
x22 = 47.1238898038469
x23 = 7517042.68028432
x24 = 78.5398163397448
x25 = 53.4070751110265
x26 = -72.2566310325652
x27 = -160.221225333079
x28 = 91.106186954104
x29 = -9591.28237140964
x30 = 59.6902604182061
x31 = -28.2743338823081
x32 = -65.9734457253857
x33 = -21.9911485751286
x34 = 97.3893722612836
x35 = -59.6902604182061
x35 = -59.6902604182061
The graph