Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation cos(x)=-2
-
Equation 17x-8=20x+7
-
Equation 9*(x-5)=-x
-
Equation x^2+2x-3=0
- Express {x} in terms of y where:
- 7*x+19*y=12
- 2*x+2*y=-6
- 10*x-2*y=0
- 12*x-13*y=-14
- Integral of d{x}:
- cos(x/4)
- Derivative of:
-
cos(x/4)
-
sqrt(3)/2
- Limit of the function:
-
sqrt(3)/2
-
Identical expressions
- cos(x/ four)=sqrt(three)/ two
- co sinus of e of (x divide by 4) equally square root of (3) divide by 2
- co sinus of e of (x divide by four) equally square root of (three) divide by two
- cos(x/4)=√(3)/2
- cosx/4=sqrt3/2
- cos(x divide by 4)=sqrt(3) divide by 2
-
Similar expressions
- sin(x)+sqrt((2-sqrt3)/2*(cos(x)+1))=0
- cos(x)=-sqrt3/2
- (sinx/4)^2+2*sinx/4*cosx/4+(cosx/4)^2=0
- sin(3x+(pi/13))=sqrt3/2
cos(x/4)=sqrt(3)/2 equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
___ /x\ \/ 3 cos|-| = ----- \4/ 2
$$\cos{\left(\frac{x}{4} \right)} = \frac{\sqrt{3}}{2}$$
Detail solution
Given the equation
$$\cos{\left(\frac{x}{4} \right)} = \frac{\sqrt{3}}{2}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$\frac{x}{4} = \pi n + \operatorname{acos}{\left(\frac{\sqrt{3}}{2} \right)}$$
$$\frac{x}{4} = \pi n - \pi + \operatorname{acos}{\left(\frac{\sqrt{3}}{2} \right)}$$
Or
$$\frac{x}{4} = \pi n + \frac{\pi}{6}$$
$$\frac{x}{4} = \pi n - \frac{5 \pi}{6}$$
, where n - is a integer
Divide both parts of the equation by
$$\frac{1}{4}$$
we get the answer:
$$x_{1} = 4 \pi n + \frac{2 \pi}{3}$$
$$x_{2} = 4 \pi n - \frac{10 \pi}{3}$$
$$\cos{\left(\frac{x}{4} \right)} = \frac{\sqrt{3}}{2}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$\frac{x}{4} = \pi n + \operatorname{acos}{\left(\frac{\sqrt{3}}{2} \right)}$$
$$\frac{x}{4} = \pi n - \pi + \operatorname{acos}{\left(\frac{\sqrt{3}}{2} \right)}$$
Or
$$\frac{x}{4} = \pi n + \frac{\pi}{6}$$
$$\frac{x}{4} = \pi n - \frac{5 \pi}{6}$$
, where n - is a integer
Divide both parts of the equation by
$$\frac{1}{4}$$
we get the answer:
$$x_{1} = 4 \pi n + \frac{2 \pi}{3}$$
$$x_{2} = 4 \pi n - \frac{10 \pi}{3}$$
Sum and product of roots
[src]
sum
2*pi 22*pi ---- + ----- 3 3
$$\frac{2 \pi}{3} + \frac{22 \pi}{3}$$
=
8*pi
$$8 \pi$$
product
2*pi 22*pi ----*----- 3 3
$$\frac{2 \pi}{3} \frac{22 \pi}{3}$$
=
2 44*pi ------ 9
$$\frac{44 \pi^{2}}{9}$$
44*pi^2/9
Rapid solution
[src]
2*pi
x1 = ----
3
$$x_{1} = \frac{2 \pi}{3}$$
22*pi
x2 = -----
3
$$x_{2} = \frac{22 \pi}{3}$$
x2 = 22*pi/3
Numerical answer
[src]
x1 = -580.147443362915
x2 = -77.4926187885482
x3 = 2.0943951023932
x4 = 23.0383461263252
x5 = 379.085513533168
x6 = -23.0383461263252
x7 = 102.625360017267
x8 = 27.2271363311115
x9 = 52.3598775598299
x10 = 73.3038285837618
x11 = 98.4365698124802
x12 = -73.3038285837618
x13 = 77.4926187885482
x14 = -27.2271363311115
x15 = -8241.44472791722
x16 = -102.625360017267
x17 = -98.4365698124802
x18 = -2.0943951023932
x19 = 2892.359636405
x20 = -52.3598775598299
x21 = 274.365758413509
x22 = -3064.10003480124
x23 = 3470.41268466552
x24 = 48.1710873550435
x25 = -123.569311041199
x26 = -48.1710873550435
x27 = -152.890842474703
x27 = -152.890842474703
The graph