Mister Exam
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How to use it?
- Equation:
- Equation (d+7)(-d-7)+(2d-1)
- Equation sin(pi(x+4)/6)=-0.5
- Equation x^4-17x^2+16=0
- Equation 2x^2-50=0
- Express {x} in terms of y where:
- (x^2+y^2-1)^3+x^2*y^3=0
- -1*x-19*y=-10
- 4*x-16*y=6
- 5*x+5*y=20
- Canonical form:
- -0.5
- Sum of series:
-
-0.5
- -0.5
-
Identical expressions
- sin(pi(x+ four)/ six)=- zero . five
- sinus of ( Pi (x plus 4) divide by 6) equally minus 0.5
- sinus of ( Pi (x plus four) divide by six) equally minus zero . five
- sinpix+4/6=-0.5
- sin(pi(x+4) divide by 6)=-0.5
-
Similar expressions
- sin(pi(x-4)/6)=-0.5
- sin(pi(x+4)/6)=+0.5
sin(pi(x+4)/6)=-0.5 equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
/pi*(x + 4)\ sin|----------| = -1/2 \ 6 /
$$\sin{\left(\frac{\pi \left(x + 4\right)}{6} \right)} = - \frac{1}{2}$$
Detail solution
Given the equation
$$\sin{\left(\frac{\pi \left(x + 4\right)}{6} \right)} = - \frac{1}{2}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$\frac{\pi x}{6} + \frac{\pi}{6} = \pi n + \operatorname{acos}{\left(- \frac{1}{2} \right)}$$
$$\frac{\pi x}{6} + \frac{\pi}{6} = \pi n - \pi + \operatorname{acos}{\left(- \frac{1}{2} \right)}$$
Or
$$\frac{\pi x}{6} + \frac{\pi}{6} = \pi n + \frac{2 \pi}{3}$$
$$\frac{\pi x}{6} + \frac{\pi}{6} = \pi n - \frac{\pi}{3}$$
, where n - is a integer
Move
$$\frac{\pi}{6}$$
to right part of the equation
with the opposite sign, in total:
$$\frac{\pi x}{6} = \pi n + \frac{\pi}{2}$$
$$\frac{\pi x}{6} = \pi n - \frac{\pi}{2}$$
Divide both parts of the equation by
$$\frac{\pi}{6}$$
we get the answer:
$$x_{1} = \frac{6 \left(\pi n + \frac{\pi}{2}\right)}{\pi}$$
$$x_{2} = \frac{6 \left(\pi n - \frac{\pi}{2}\right)}{\pi}$$
$$\sin{\left(\frac{\pi \left(x + 4\right)}{6} \right)} = - \frac{1}{2}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$\frac{\pi x}{6} + \frac{\pi}{6} = \pi n + \operatorname{acos}{\left(- \frac{1}{2} \right)}$$
$$\frac{\pi x}{6} + \frac{\pi}{6} = \pi n - \pi + \operatorname{acos}{\left(- \frac{1}{2} \right)}$$
Or
$$\frac{\pi x}{6} + \frac{\pi}{6} = \pi n + \frac{2 \pi}{3}$$
$$\frac{\pi x}{6} + \frac{\pi}{6} = \pi n - \frac{\pi}{3}$$
, where n - is a integer
Move
$$\frac{\pi}{6}$$
to right part of the equation
with the opposite sign, in total:
$$\frac{\pi x}{6} = \pi n + \frac{\pi}{2}$$
$$\frac{\pi x}{6} = \pi n - \frac{\pi}{2}$$
Divide both parts of the equation by
$$\frac{\pi}{6}$$
we get the answer:
$$x_{1} = \frac{6 \left(\pi n + \frac{\pi}{2}\right)}{\pi}$$
$$x_{2} = \frac{6 \left(\pi n - \frac{\pi}{2}\right)}{\pi}$$
Sum and product of roots
[src]
sum
3 + 7
$$3 + 7$$
=
10
$$10$$
product
3*7
$$3 \cdot 7$$
=
21
$$21$$
21
Numerical answer
[src]
x1 = -5.0
x2 = -21.0
x3 = 63.0
x4 = 67.0
x5 = -81.0
x6 = 3.0
x7 = 39.0
x8 = 15.0
x9 = 27.0
x10 = -53.0
x11 = 51.0
x12 = -89.0
x13 = -17.0
x14 = 19.0
x15 = -93.0
x16 = -101.0
x17 = -105.0
x18 = 31.0
x19 = -65.0
x20 = 55.0
x21 = -9.0
x22 = -69.0
x23 = 87.0
x24 = -29.0
x25 = 79.0
x26 = -33.0
x27 = 99.0
x28 = 7.0
x29 = -77.0
x30 = -57.0
x31 = -45.0
x32 = 43.0
x33 = 91.0
x34 = -41.0
x35 = 75.0
x35 = 75.0