Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation sin(x/3)=-1/2
-
Equation x^3+4*x^2-x-4=0
-
Equation 2^2-x-1=x^2-5*x-(-1-x^2)
-
Equation (7x-8)-(2x-5)=17
- Express {x} in terms of y where:
- -14*x-16*y=14
- 16*x-17*y=-9
- -14*x-3*y=-5
- -16*x-20*y=6
- Graphing y =:
- sin(x/3)
- Integral of d{x}:
-
sin(x/3)
-
-1/2
- Limit of the function:
-
sin(x/3)
- -1/2
- Derivative of:
- -1/2
-
Identical expressions
- sin(x/ three)=- one / two
- sinus of (x divide by 3) equally minus 1 divide by 2
- sinus of (x divide by three) equally minus one divide by two
- sinx/3=-1/2
- sin(x divide by 3)=-1 divide by 2
-
Similar expressions
- sin(x/3+пи/6)=1/2
- sin(x/3)=+1/2
- arcsin(x)/3=pi
- 2*sin(x/3-pi/4)=3
- sin(x-(1/2))-x+(1/2)=0
- cos(x)=-(1/2)
- sin(x/3+pi/18)=-1
sin(x/3)=-1/2 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$\sin{\left(\frac{x}{3} \right)} = - \frac{1}{2}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$\frac{x}{3} = 2 \pi n + \operatorname{asin}{\left(- \frac{1}{2} \right)}$$
$$\frac{x}{3} = 2 \pi n - \operatorname{asin}{\left(- \frac{1}{2} \right)} + \pi$$
Or
$$\frac{x}{3} = 2 \pi n - \frac{\pi}{6}$$
$$\frac{x}{3} = 2 \pi n + \frac{7 \pi}{6}$$
, where n - is a integer
Divide both parts of the equation by
$$\frac{1}{3}$$
we get the answer:
$$x_{1} = 6 \pi n - \frac{\pi}{2}$$
$$x_{2} = 6 \pi n + \frac{7 \pi}{2}$$
$$\sin{\left(\frac{x}{3} \right)} = - \frac{1}{2}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$\frac{x}{3} = 2 \pi n + \operatorname{asin}{\left(- \frac{1}{2} \right)}$$
$$\frac{x}{3} = 2 \pi n - \operatorname{asin}{\left(- \frac{1}{2} \right)} + \pi$$
Or
$$\frac{x}{3} = 2 \pi n - \frac{\pi}{6}$$
$$\frac{x}{3} = 2 \pi n + \frac{7 \pi}{6}$$
, where n - is a integer
Divide both parts of the equation by
$$\frac{1}{3}$$
we get the answer:
$$x_{1} = 6 \pi n - \frac{\pi}{2}$$
$$x_{2} = 6 \pi n + \frac{7 \pi}{2}$$
Rapid solution
[src]
-pi
x1 = ----
2
$$x_{1} = - \frac{\pi}{2}$$
7*pi
x2 = ----
2
$$x_{2} = \frac{7 \pi}{2}$$
x2 = 7*pi/2
Sum and product of roots
[src]
sum
pi 7*pi - -- + ---- 2 2
$$- \frac{\pi}{2} + \frac{7 \pi}{2}$$
=
3*pi
$$3 \pi$$
product
-pi 7*pi ----*---- 2 2
$$- \frac{\pi}{2} \frac{7 \pi}{2}$$
=
2 -7*pi ------ 4
$$- \frac{7 \pi^{2}}{4}$$
-7*pi^2/4
Numerical answer
[src]
x1 = -76.9690200129499
x2 = -359.712358836031
x3 = 86.3937979737193
x4 = -39.2699081698724
x5 = -58.1194640914112
x6 = -83.2522053201295
x7 = 92.6769832808989
x8 = -20.4203522483337
x9 = -102.101761241668
x10 = 67.5442420521806
x11 = -26.7035375555132
x12 = -64.4026493985908
x13 = -1.5707963267949
x14 = 17.2787595947439
x15 = -95.8185759344887
x16 = 10.9955742875643
x17 = 36.1283155162826
x18 = 48.6946861306418
x19 = 111.526539202438
x20 = -7.85398163397448
x21 = 73.8274273593601
x22 = 29.845130209103
x23 = -45.553093477052
x24 = 54.9778714378214
x24 = 54.9778714378214
The graph