Mister Exam
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How to use it?
- Equation:
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Equation (25+x)-10=40
-
Equation x^3+5*x^2-4*x-20=0
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Equation x^2+4*x=21
-
Equation x^3+x-1=0
- Express {x} in terms of y where:
- 13*x+3*y=6
- -9*x+1*y=20
- 7*x-18*y=-4
- 5*x-13*y=-1
-
Identical expressions
- sin(two x/ seven)=-√ two /2
- sinus of (2x divide by 7) equally minus √2 divide by 2
- sinus of (two x divide by seven) equally minus √ two divide by 2
- sin2x/7=-√2/2
- sin(2x divide by 7)=-√2 divide by 2
-
Similar expressions
- sin(2x/7)=+√2/2
- 16*cos(2*x/7)*(sin(2*x/7))^2-9=0
sin(2x/7)=-√2/2 equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
___ /2*x\ -\/ 2 sin|---| = ------- \ 7 / 2
$$\sin{\left(\frac{2 x}{7} \right)} = \frac{\left(-1\right) \sqrt{2}}{2}$$
Detail solution
Given the equation
$$\sin{\left(\frac{2 x}{7} \right)} = \frac{\left(-1\right) \sqrt{2}}{2}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$\frac{2 x}{7} = 2 \pi n + \operatorname{asin}{\left(- \frac{\sqrt{2}}{2} \right)}$$
$$\frac{2 x}{7} = 2 \pi n - \operatorname{asin}{\left(- \frac{\sqrt{2}}{2} \right)} + \pi$$
Or
$$\frac{2 x}{7} = 2 \pi n - \frac{\pi}{4}$$
$$\frac{2 x}{7} = 2 \pi n + \frac{5 \pi}{4}$$
, where n - is a integer
Divide both parts of the equation by
$$\frac{2}{7}$$
we get the answer:
$$x_{1} = 7 \pi n - \frac{7 \pi}{8}$$
$$x_{2} = 7 \pi n + \frac{35 \pi}{8}$$
$$\sin{\left(\frac{2 x}{7} \right)} = \frac{\left(-1\right) \sqrt{2}}{2}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$\frac{2 x}{7} = 2 \pi n + \operatorname{asin}{\left(- \frac{\sqrt{2}}{2} \right)}$$
$$\frac{2 x}{7} = 2 \pi n - \operatorname{asin}{\left(- \frac{\sqrt{2}}{2} \right)} + \pi$$
Or
$$\frac{2 x}{7} = 2 \pi n - \frac{\pi}{4}$$
$$\frac{2 x}{7} = 2 \pi n + \frac{5 \pi}{4}$$
, where n - is a integer
Divide both parts of the equation by
$$\frac{2}{7}$$
we get the answer:
$$x_{1} = 7 \pi n - \frac{7 \pi}{8}$$
$$x_{2} = 7 \pi n + \frac{35 \pi}{8}$$
Sum and product of roots
[src]
sum
7*pi 35*pi - ---- + ----- 8 8
$$- \frac{7 \pi}{8} + \frac{35 \pi}{8}$$
=
7*pi ---- 2
$$\frac{7 \pi}{2}$$
product
-7*pi 35*pi -----*----- 8 8
$$- \frac{7 \pi}{8} \frac{35 \pi}{8}$$
=
2 -245*pi -------- 64
$$- \frac{245 \pi^{2}}{64}$$
-245*pi^2/64
Rapid solution
[src]
-7*pi
x1 = -----
8
$$x_{1} = - \frac{7 \pi}{8}$$
35*pi
x2 = -----
8
$$x_{2} = \frac{35 \pi}{8}$$
x2 = 35*pi/8
Numerical answer
[src]
x1 = 63.2245521534946
x2 = 19.2422550032375
x3 = -74.2201264410589
x4 = -68.7223392972767
x5 = -2.74889357189107
x6 = 343.611696486384
x7 = -90.7134878724053
x8 = -96.2112750161874
x9 = 79.717913584841
x10 = 85.2157007286231
x11 = -46.7311907221482
x12 = 101.70906215997
x13 = 41.233403578366
x14 = 123.700210735098
x15 = 35.7356164345839
x16 = -8.24668071567321
x17 = 57.7267650097125
x18 = -24.7400421470196
x19 = 13.7444678594553
x20 = -52.2289778659303
x21 = -30.2378292908018
x21 = -30.2378292908018