Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation x-6/x=-1
- Equation 1-y^2=2+x
-
Equation 1-7*(4+2*x)=-9-4*x
-
Equation sin(x)=2
- Express {x} in terms of y where:
- 4*x+3*y=-15
- -6*x+1*y=14
- 1*x+7*y=8
- 20*x-4*y=-7
- Sum of series:
-
1/2
- Integral of d{x}:
-
1/2
- Derivative of:
-
1/2
-
Identical expressions
- cos(pi*(x- one)/ three)= one / two
- co sinus of e of ( Pi multiply by (x minus 1) divide by 3) equally 1 divide by 2
- co sinus of e of ( Pi multiply by (x minus one) divide by three) equally one divide by two
- cos(pi(x-1)/3)=1/2
- cospix-1/3=1/2
- cos(pi*(x-1) divide by 3)=1 divide by 2
-
Similar expressions
- cos(pi*(x+1)/3)=1/2
cos(pi*(x-1)/3)=1/2 equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
/pi*(x - 1)\ cos|----------| = 1/2 \ 3 /
$$\cos{\left(\frac{\pi \left(x - 1\right)}{3} \right)} = \frac{1}{2}$$
Detail solution
Given the equation
$$\cos{\left(\frac{\pi \left(x - 1\right)}{3} \right)} = \frac{1}{2}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$\frac{\pi x}{3} + \frac{\pi}{6} = 2 \pi n + \operatorname{asin}{\left(\frac{1}{2} \right)}$$
$$\frac{\pi x}{3} + \frac{\pi}{6} = 2 \pi n - \operatorname{asin}{\left(\frac{1}{2} \right)} + \pi$$
Or
$$\frac{\pi x}{3} + \frac{\pi}{6} = 2 \pi n + \frac{\pi}{6}$$
$$\frac{\pi x}{3} + \frac{\pi}{6} = 2 \pi n + \frac{5 \pi}{6}$$
, where n - is a integer
Move
$$\frac{\pi}{6}$$
to right part of the equation
with the opposite sign, in total:
$$\frac{\pi x}{3} = 2 \pi n$$
$$\frac{\pi x}{3} = 2 \pi n + \frac{2 \pi}{3}$$
Divide both parts of the equation by
$$\frac{\pi}{3}$$
we get the answer:
$$x_{1} = 6 n$$
$$x_{2} = \frac{3 \cdot \left(2 \pi n + \frac{2 \pi}{3}\right)}{\pi}$$
$$\cos{\left(\frac{\pi \left(x - 1\right)}{3} \right)} = \frac{1}{2}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$\frac{\pi x}{3} + \frac{\pi}{6} = 2 \pi n + \operatorname{asin}{\left(\frac{1}{2} \right)}$$
$$\frac{\pi x}{3} + \frac{\pi}{6} = 2 \pi n - \operatorname{asin}{\left(\frac{1}{2} \right)} + \pi$$
Or
$$\frac{\pi x}{3} + \frac{\pi}{6} = 2 \pi n + \frac{\pi}{6}$$
$$\frac{\pi x}{3} + \frac{\pi}{6} = 2 \pi n + \frac{5 \pi}{6}$$
, where n - is a integer
Move
$$\frac{\pi}{6}$$
to right part of the equation
with the opposite sign, in total:
$$\frac{\pi x}{3} = 2 \pi n$$
$$\frac{\pi x}{3} = 2 \pi n + \frac{2 \pi}{3}$$
Divide both parts of the equation by
$$\frac{\pi}{3}$$
we get the answer:
$$x_{1} = 6 n$$
$$x_{2} = \frac{3 \cdot \left(2 \pi n + \frac{2 \pi}{3}\right)}{\pi}$$
Sum and product of roots
[src]
sum
0 + 0 + 2
$$\left(0 + 0\right) + 2$$
=
2
$$2$$
product
1*0*2
$$1 \cdot 0 \cdot 2$$
=
0
$$0$$
0
Numerical answer
[src]
x1 = -24.0
x2 = 32.0
x3 = 408.0
x4 = 24.0
x5 = 6.0
x6 = 36.0
x7 = 14.0
x8 = 86.0
x9 = -88.0
x10 = -100.0
x11 = 98.0
x12 = -12.0
x13 = -58.0
x14 = 464.0
x15 = -96.0
x16 = -76.0
x17 = 90.0
x18 = 26.0
x19 = -34.0
x20 = -10.0
x21 = -60.0
x22 = 500.0
x23 = 440.0
x24 = -22.0
x25 = 12.0
x26 = -28.0
x27 = 66.0
x28 = -6.0
x29 = -82.0
x30 = 38.0
x31 = -94.0
x32 = -4.0
x33 = -30.0
x34 = 960.0
x35 = 84.0
x36 = 60.0
x37 = 8.0
x38 = 18.0
x39 = 20.0
x40 = 80.0
x41 = -40.0
x42 = 552.0
x43 = 30.0
x44 = -42.0
x45 = -16.0
x46 = -46.0
x47 = 92.0
x48 = 50.0
x49 = -36.0
x50 = 522.0
x51 = 96.0
x52 = 56.0
x53 = 68.0
x54 = -84.0
x55 = -70.0
x56 = 62.0
x57 = -78.0
x58 = 482.0
x59 = -72.0
x60 = -90.0
x61 = 2.0
x62 = 42.0
x63 = -64.0
x64 = 44.0
x65 = -54.0
x66 = 638.0
x67 = 48.0
x68 = 72.0
x69 = 54.0
x70 = -48.0
x71 = -52.0
x72 = 0.0
x73 = 74.0
x74 = -18.0
x75 = 78.0
x76 = -66.0
x76 = -66.0
The graph