Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation sin(x/4)=1/2
-
Equation x*log(x)=0
- Equation sin(x)-cos(x)=0.7
-
Equation x^4+15x^2-16=0
- Express {x} in terms of y where:
- 14*x-16*y=14
- -10*x+18*y=6
- 4*x+13*y=13
- 17*x-19*y=1
- Graphing y =:
- sin(x/4)
- Derivative of:
-
sin(x/4)
-
1/2
- Integral of d{x}:
-
sin(x/4)
-
1/2
- Sum of series:
-
1/2
-
Identical expressions
- sin(x/ four)= one / two
- sinus of (x divide by 4) equally 1 divide by 2
- sinus of (x divide by four) equally one divide by two
- sinx/4=1/2
- sin(x divide by 4)=1 divide by 2
-
Similar expressions
- 6*sin(x/4-pi/12)-6=0
- sinx/4=-sqrt2/2
- sin(x/4-pi/8)=0
- (sqrt3*tgx+1)/(2*sinx-1)=0
sin(x/4)=1/2 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$\sin{\left(\frac{x}{4} \right)} = \frac{1}{2}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$\frac{x}{4} = 2 \pi n + \operatorname{asin}{\left(\frac{1}{2} \right)}$$
$$\frac{x}{4} = 2 \pi n - \operatorname{asin}{\left(\frac{1}{2} \right)} + \pi$$
Or
$$\frac{x}{4} = 2 \pi n + \frac{\pi}{6}$$
$$\frac{x}{4} = 2 \pi n + \frac{5 \pi}{6}$$
, where n - is a integer
Divide both parts of the equation by
$$\frac{1}{4}$$
we get the answer:
$$x_{1} = 8 \pi n + \frac{2 \pi}{3}$$
$$x_{2} = 8 \pi n + \frac{10 \pi}{3}$$
$$\sin{\left(\frac{x}{4} \right)} = \frac{1}{2}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$\frac{x}{4} = 2 \pi n + \operatorname{asin}{\left(\frac{1}{2} \right)}$$
$$\frac{x}{4} = 2 \pi n - \operatorname{asin}{\left(\frac{1}{2} \right)} + \pi$$
Or
$$\frac{x}{4} = 2 \pi n + \frac{\pi}{6}$$
$$\frac{x}{4} = 2 \pi n + \frac{5 \pi}{6}$$
, where n - is a integer
Divide both parts of the equation by
$$\frac{1}{4}$$
we get the answer:
$$x_{1} = 8 \pi n + \frac{2 \pi}{3}$$
$$x_{2} = 8 \pi n + \frac{10 \pi}{3}$$
Rapid solution
[src]
2*pi
x1 = ----
3
$$x_{1} = \frac{2 \pi}{3}$$
10*pi
x2 = -----
3
$$x_{2} = \frac{10 \pi}{3}$$
x2 = 10*pi/3
Sum and product of roots
[src]
sum
2*pi 10*pi ---- + ----- 3 3
$$\frac{2 \pi}{3} + \frac{10 \pi}{3}$$
=
4*pi
$$4 \pi$$
product
2*pi 10*pi ----*----- 3 3
$$\frac{2 \pi}{3} \frac{10 \pi}{3}$$
=
2 20*pi ------ 9
$$\frac{20 \pi^{2}}{9}$$
20*pi^2/9
Numerical answer
[src]
x1 = 228.289066160858
x2 = 3570.9436495804
x3 = 2.0943951023932
x4 = -14.6607657167524
x5 = -23.0383461263252
x6 = 102.625360017267
x7 = 27.2271363311115
x8 = -90.0589894029074
x9 = 52.3598775598299
x10 = 35.6047167406843
x11 = 60.7374579694027
x12 = -73.3038285837618
x13 = 77.4926187885482
x14 = 85.870199198121
x15 = 10.471975511966
x16 = -98.4365698124802
x17 = -64.9262481741891
x18 = -48.1710873550435
x19 = -39.7935069454707
x19 = -39.7935069454707
The graph