Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation 4x^2-3x=0
-
Equation cos(x/8+pi/4)=1
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Equation 8x^2=0
- Equation sin(0.5x)=-sqrt3/2
- Express {x} in terms of y where:
- 10*x-1*y=10
- 15*x-17*y=19
- 9*x-8*y=6
- 15*x+15*y=16
-
Identical expressions
- sin((pi*(x+ nine))/ four)=sqrt(two)/(- two)
- sinus of (( Pi multiply by (x plus 9)) divide by 4) equally square root of (2) divide by ( minus 2)
- sinus of (( Pi multiply by (x plus nine)) divide by four) equally square root of (two) divide by ( minus two)
- sin((pi*(x+9))/4)=√(2)/(-2)
- sin((pi(x+9))/4)=sqrt(2)/(-2)
- sinpix+9/4=sqrt2/-2
- sin((pi*(x+9)) divide by 4)=sqrt(2) divide by (-2)
-
Similar expressions
- sin((pi*(x-9))/4)=sqrt(2)/(-2)
- sin((pi*(x+9))/4)=sqrt(2)/(2)
sin((pi*(x+9))/4)=sqrt(2)/(-2) equation
The teacher will be very surprised to see your correct solution 😉
The solution
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[src]
___ /pi*(x + 9)\ \/ 2 sin|----------| = ----- \ 4 / -2
$$\sin{\left(\frac{\pi \left(x + 9\right)}{4} \right)} = \frac{\sqrt{2}}{-2}$$
Detail solution
Given the equation
$$\sin{\left(\frac{\pi \left(x + 9\right)}{4} \right)} = \frac{\sqrt{2}}{-2}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$\frac{\pi x}{4} + \frac{\pi}{4} = 2 \pi n + \operatorname{asin}{\left(- \frac{\sqrt{2}}{2} \right)}$$
$$\frac{\pi x}{4} + \frac{\pi}{4} = 2 \pi n - \operatorname{asin}{\left(- \frac{\sqrt{2}}{2} \right)} + \pi$$
Or
$$\frac{\pi x}{4} + \frac{\pi}{4} = 2 \pi n - \frac{\pi}{4}$$
$$\frac{\pi x}{4} + \frac{\pi}{4} = 2 \pi n + \frac{5 \pi}{4}$$
, where n - is a integer
Move
$$\frac{\pi}{4}$$
to right part of the equation
with the opposite sign, in total:
$$\frac{\pi x}{4} = 2 \pi n - \frac{\pi}{2}$$
$$\frac{\pi x}{4} = 2 \pi n + \pi$$
Divide both parts of the equation by
$$\frac{\pi}{4}$$
we get the answer:
$$x_{1} = \frac{4 \cdot \left(2 \pi n - \frac{\pi}{2}\right)}{\pi}$$
$$x_{2} = \frac{4 \cdot \left(2 \pi n + \pi\right)}{\pi}$$
$$\sin{\left(\frac{\pi \left(x + 9\right)}{4} \right)} = \frac{\sqrt{2}}{-2}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$\frac{\pi x}{4} + \frac{\pi}{4} = 2 \pi n + \operatorname{asin}{\left(- \frac{\sqrt{2}}{2} \right)}$$
$$\frac{\pi x}{4} + \frac{\pi}{4} = 2 \pi n - \operatorname{asin}{\left(- \frac{\sqrt{2}}{2} \right)} + \pi$$
Or
$$\frac{\pi x}{4} + \frac{\pi}{4} = 2 \pi n - \frac{\pi}{4}$$
$$\frac{\pi x}{4} + \frac{\pi}{4} = 2 \pi n + \frac{5 \pi}{4}$$
, where n - is a integer
Move
$$\frac{\pi}{4}$$
to right part of the equation
with the opposite sign, in total:
$$\frac{\pi x}{4} = 2 \pi n - \frac{\pi}{2}$$
$$\frac{\pi x}{4} = 2 \pi n + \pi$$
Divide both parts of the equation by
$$\frac{\pi}{4}$$
we get the answer:
$$x_{1} = \frac{4 \cdot \left(2 \pi n - \frac{\pi}{2}\right)}{\pi}$$
$$x_{2} = \frac{4 \cdot \left(2 \pi n + \pi\right)}{\pi}$$
Sum and product of roots
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sum
0 - 2 + 4
$$\left(-2 + 0\right) + 4$$
=
2
$$2$$
product
1*-2*4
$$1 \left(-2\right) 4$$
=
-8
$$-8$$
-8
Numerical answer
[src]
x1 = 86.0
x2 = -10.0
x3 = -82.0
x4 = -42.0
x5 = -100.0
x6 = -92.0
x7 = -20.0
x8 = -34.0
x9 = -18.0
x10 = -60.0
x11 = -68.0
x12 = 68.0
x13 = -90.0
x14 = 20.0
x15 = 44.0
x16 = -44.0
x17 = -28.0
x18 = 78.0
x19 = 14.0
x20 = -84.0
x21 = 36.0
x22 = 84.0
x23 = -36.0
x24 = -2.0
x25 = 4.0
x26 = -98.0
x27 = 70.0
x28 = -4.0
x29 = 54.0
x30 = -52.0
x31 = 100.0
x32 = 94.0
x33 = 46.0
x34 = 62.0
x35 = -74.0
x36 = 52.0
x37 = 12.0
x38 = -12.0
x39 = 92.0
x40 = 6.0
x41 = 76.0
x42 = 22.0
x43 = -66.0
x44 = -76.0
x45 = -26.0
x46 = 30.0
x47 = -50.0
x48 = 28.0
x49 = 60.0
x50 = 38.0
x51 = -58.0
x51 = -58.0
The graph