Mister Exam
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How to use it?
- Equation:
-
Equation x^4-x^3+5*x^2=0
-
Equation 5-2*x=11-7*(x+2)
- Equation sin(-x/3)=sqrt(2)/2
- Equation 2+√2sin(x)=0
- Express {x} in terms of y where:
- 1*x-19*y=-10
- -10*x-9*y=-6
- 20*x-8*y=13
- -10*x+18*y=6
- Limit of the function:
-
sqrt(2)/2
- sqrt(2)/2
-
Identical expressions
- sin(-x/ three)=sqrt(two)/ two
- sinus of ( minus x divide by 3) equally square root of (2) divide by 2
- sinus of ( minus x divide by three) equally square root of (two) divide by two
- sin(-x/3)=√(2)/2
- sin-x/3=sqrt2/2
- sin(-x divide by 3)=sqrt(2) divide by 2
-
Similar expressions
- sin(x)=-sqrt2/2
- sin(x/3)=sqrt(2)/2
- sinx/4=-sqrt2/2
sin(-x/3)=sqrt(2)/2 equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
___ /-x \ \/ 2 sin|---| = ----- \ 3 / 2
$$\sin{\left(\frac{\left(-1\right) x}{3} \right)} = \frac{\sqrt{2}}{2}$$
Detail solution
Given the equation
$$\sin{\left(\frac{\left(-1\right) x}{3} \right)} = \frac{\sqrt{2}}{2}$$
- this is the simplest trigonometric equation
The equation is transformed to
$$\sin{\left(\frac{x}{3} \right)} = - \frac{\sqrt{2}}{2}$$
This equation is transformed to
$$\frac{x}{3} = 2 \pi n + \operatorname{asin}{\left(- \frac{\sqrt{2}}{2} \right)}$$
$$\frac{x}{3} = 2 \pi n - \operatorname{asin}{\left(- \frac{\sqrt{2}}{2} \right)} + \pi$$
Or
$$\frac{x}{3} = 2 \pi n - \frac{\pi}{4}$$
$$\frac{x}{3} = 2 \pi n + \frac{5 \pi}{4}$$
, where n - is a integer
Divide both parts of the equation by
$$\frac{1}{3}$$
we get the answer:
$$x_{1} = 6 \pi n - \frac{3 \pi}{4}$$
$$x_{2} = 6 \pi n + \frac{15 \pi}{4}$$
$$\sin{\left(\frac{\left(-1\right) x}{3} \right)} = \frac{\sqrt{2}}{2}$$
- this is the simplest trigonometric equation
Divide both parts of the equation by -1
The equation is transformed to
$$\sin{\left(\frac{x}{3} \right)} = - \frac{\sqrt{2}}{2}$$
This equation is transformed to
$$\frac{x}{3} = 2 \pi n + \operatorname{asin}{\left(- \frac{\sqrt{2}}{2} \right)}$$
$$\frac{x}{3} = 2 \pi n - \operatorname{asin}{\left(- \frac{\sqrt{2}}{2} \right)} + \pi$$
Or
$$\frac{x}{3} = 2 \pi n - \frac{\pi}{4}$$
$$\frac{x}{3} = 2 \pi n + \frac{5 \pi}{4}$$
, where n - is a integer
Divide both parts of the equation by
$$\frac{1}{3}$$
we get the answer:
$$x_{1} = 6 \pi n - \frac{3 \pi}{4}$$
$$x_{2} = 6 \pi n + \frac{15 \pi}{4}$$
Sum and product of roots
[src]
sum
3*pi 15*pi - ---- + ----- 4 4
$$- \frac{3 \pi}{4} + \frac{15 \pi}{4}$$
=
3*pi
$$3 \pi$$
product
-3*pi 15*pi -----*----- 4 4
$$- \frac{3 \pi}{4} \frac{15 \pi}{4}$$
=
2 -45*pi ------- 16
$$- \frac{45 \pi^{2}}{16}$$
-45*pi^2/16
Rapid solution
[src]
-3*pi
x1 = -----
4
$$x_{1} = - \frac{3 \pi}{4}$$
15*pi
x2 = -----
4
$$x_{2} = \frac{15 \pi}{4}$$
x2 = 15*pi/4
Numerical answer
[src]
x1 = -473.595092528661
x2 = -101.316363078271
x3 = -96.6039740978861
x4 = -44.7676953136546
x5 = 11.7809724509617
x6 = -1703.52861640907
x7 = -134.303085940964
x8 = 1142.75432774329
x9 = -58.9048622548086
x10 = 30.6305283725005
x11 = 256.825199430966
x12 = -82.4668071567321
x13 = 73.0420291959627
x14 = -77.7544181763474
x15 = 68.329640215578
x16 = 16.4933614313464
x17 = 35.3429173528852
x18 = -2.35619449019234
x19 = -21.2057504117311
x20 = -7.06858347057703
x21 = 49.4800842940392
x22 = -25.9181393921158
x23 = 539.568538254047
x24 = 2179.47990342792
x25 = -40.0553063332699
x26 = -63.6172512351933
x27 = -3305.74086973986
x28 = 54.1924732744239
x29 = 91.8915851175014
x30 = 13376.1161208219
x31 = 87.1791961371168
x31 = 87.1791961371168