Mister Exam
Other calculators
-
How to use it?
- Equation:
- Equation x-y=2
-
Equation x^3+2x^2-x-2=0
- Equation (x+20)*(-x+10)=0
-
Equation x^2+8*x+15=0
- Express {x} in terms of y where:
- 15*x+7*y=2
- 12*x-20*y=10
- -17*x-15*y=-17
- 6*x-2*y=20
- Graphing y =:
- cos(x/2)
- Derivative of:
-
cos(x/2)
- Limit of the function:
-
cos(x/2)
-
sqrt(2)/2
- sqrt(2)/2
-
Identical expressions
- cos(x/ two)=sqrt(two)/ two
- co sinus of e of (x divide by 2) equally square root of (2) divide by 2
- co sinus of e of (x divide by two) equally square root of (two) divide by two
- cos(x/2)=√(2)/2
- cosx/2=sqrt2/2
- cos(x divide by 2)=sqrt(2) divide by 2
-
Similar expressions
- cos((x/2)-(pi/4))=1
- cos(x/2+pi/4)=0
- cos((x/2)-pi/4)=0
- cos((x)/(2)-(pi)/(4))=-1
- sin((-3)*x+pi/6)=(-sqrt(2))/2
cos(x/2)=sqrt(2)/2 equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
___ /x\ \/ 2 cos|-| = ----- \2/ 2
$$\cos{\left(\frac{x}{2} \right)} = \frac{\sqrt{2}}{2}$$
Detail solution
Given the equation
$$\cos{\left(\frac{x}{2} \right)} = \frac{\sqrt{2}}{2}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$\frac{x}{2} = \pi n + \operatorname{acos}{\left(\frac{\sqrt{2}}{2} \right)}$$
$$\frac{x}{2} = \pi n - \pi + \operatorname{acos}{\left(\frac{\sqrt{2}}{2} \right)}$$
Or
$$\frac{x}{2} = \pi n + \frac{\pi}{4}$$
$$\frac{x}{2} = \pi n - \frac{3 \pi}{4}$$
, where n - is a integer
Divide both parts of the equation by
$$\frac{1}{2}$$
we get the answer:
$$x_{1} = 2 \pi n + \frac{\pi}{2}$$
$$x_{2} = 2 \pi n - \frac{3 \pi}{2}$$
$$\cos{\left(\frac{x}{2} \right)} = \frac{\sqrt{2}}{2}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$\frac{x}{2} = \pi n + \operatorname{acos}{\left(\frac{\sqrt{2}}{2} \right)}$$
$$\frac{x}{2} = \pi n - \pi + \operatorname{acos}{\left(\frac{\sqrt{2}}{2} \right)}$$
Or
$$\frac{x}{2} = \pi n + \frac{\pi}{4}$$
$$\frac{x}{2} = \pi n - \frac{3 \pi}{4}$$
, where n - is a integer
Divide both parts of the equation by
$$\frac{1}{2}$$
we get the answer:
$$x_{1} = 2 \pi n + \frac{\pi}{2}$$
$$x_{2} = 2 \pi n - \frac{3 \pi}{2}$$
Rapid solution
[src]
pi
x1 = --
2
$$x_{1} = \frac{\pi}{2}$$
7*pi
x2 = ----
2
$$x_{2} = \frac{7 \pi}{2}$$
Sum and product of roots
[src]
sum
pi 7*pi
0 + -- + ----
2 2
$$\left(0 + \frac{\pi}{2}\right) + \frac{7 \pi}{2}$$
=
4*pi
$$4 \pi$$
product
pi 7*pi 1*--*---- 2 2
$$\frac{7 \pi}{2} \cdot 1 \frac{\pi}{2}$$
=
2 7*pi ----- 4
$$\frac{7 \pi^{2}}{4}$$
7*pi^2/4
Numerical answer
[src]
x1 = 10.9955742875643
x2 = 51.8362787842316
x3 = -98.9601685880785
x4 = -89.5353906273091
x5 = -10.9955742875643
x6 = -48.6946861306418
x7 = 48.6946861306418
x8 = -12677.8971535616
x9 = -39.2699081698724
x10 = 365.995544143211
x11 = 61.261056745001
x12 = -26.7035375555132
x13 = -64.4026493985908
x14 = -36.1283155162826
x15 = -76.9690200129499
x16 = 5314.00397354714
x17 = -51.8362787842316
x18 = 64.4026493985908
x19 = 36.1283155162826
x20 = -86.3937979737193
x21 = 1.5707963267949
x22 = 76.9690200129499
x23 = 73.8274273593601
x24 = -73.8274273593601
x25 = 26.7035375555132
x26 = 39.2699081698724
x27 = -23.5619449019235
x28 = 111.526539202438
x29 = -14.1371669411541
x30 = 23.5619449019235
x31 = 14.1371669411541
x32 = 98.9601685880785
x33 = 89.5353906273091
x34 = -1.5707963267949
x35 = -61.261056745001
x36 = 86.3937979737193
x36 = 86.3937979737193
The graph