Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation 2*sin(x)=1
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Equation x/2+x=12
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Equation 3x^2-12=0
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Equation x-11=-7
- Express {x} in terms of y where:
- 18*x+19*y=7
- -4*x+4*y=-9
- -20*x+14*y=16
- -4*x+14*y=-2
- arcsin(y/(sqrt(x^2+y^2)))
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Identical expressions
- z=arcsin(y/(sqrt(x^ two +y^ two)))
- z equally arc sinus of (y divide by ( square root of (x squared plus y squared )))
- z equally arc sinus of (y divide by ( square root of (x to the power of two plus y to the power of two)))
- z=arcsin(y/(√(x^2+y^2)))
- z=arcsin(y/(sqrt(x2+y2)))
- z=arcsiny/sqrtx2+y2
- z=arcsin(y/(sqrt(x²+y²)))
- z=arcsin(y/(sqrt(x to the power of 2+y to the power of 2)))
- z=arcsiny/sqrtx^2+y^2
- z=arcsin(y divide by (sqrt(x^2+y^2)))
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Similar expressions
- z=arcsin(y/(sqrt(x^2-y^2)))
z=arcsin(y/(sqrt(x^2+y^2))) equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
/ y \
z = asin|------------|
| _________|
| / 2 2 |
\\/ x + y /
$$z = \operatorname{asin}{\left(\frac{y}{\sqrt{x^{2} + y^{2}}} \right)}$$
Detail solution
Given the equation:
$$z = \operatorname{asin}{\left(\frac{y}{\sqrt{x^{2} + y^{2}}} \right)}$$
transform:
$$z = \operatorname{asin}{\left(\frac{y}{\sqrt{x^{2} + y^{2}}} \right)}$$
Expand brackets in the right part
Looking for similar summands in the right part:
We get the answer: z = asin(y/sqrt(x^2 + y^2))
$$z = \operatorname{asin}{\left(\frac{y}{\sqrt{x^{2} + y^{2}}} \right)}$$
transform:
$$z = \operatorname{asin}{\left(\frac{y}{\sqrt{x^{2} + y^{2}}} \right)}$$
Expand brackets in the right part
z = asiny/sqrt+x+2+y+2)
Looking for similar summands in the right part:
z = asin(y/sqrt(x^2 + y^2))
We get the answer: z = asin(y/sqrt(x^2 + y^2))
The graph
Rapid solution
[src]
/ / y \\ / / y \\
z1 = I*im|asin|------------|| + re|asin|------------||
| | _________|| | | _________||
| | / 2 2 || | | / 2 2 ||
\ \\/ x + y // \ \\/ x + y //
$$z_{1} = \operatorname{re}{\left(\operatorname{asin}{\left(\frac{y}{\sqrt{x^{2} + y^{2}}} \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(\frac{y}{\sqrt{x^{2} + y^{2}}} \right)}\right)}$$
z1 = re(asin(y/sqrt(x^2 + y^2))) + i*im(asin(y/sqrt(x^2 + y^2)))
Sum and product of roots
[src]
sum
/ / y \\ / / y \\
I*im|asin|------------|| + re|asin|------------||
| | _________|| | | _________||
| | / 2 2 || | | / 2 2 ||
\ \\/ x + y // \ \\/ x + y //
$$\operatorname{re}{\left(\operatorname{asin}{\left(\frac{y}{\sqrt{x^{2} + y^{2}}} \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(\frac{y}{\sqrt{x^{2} + y^{2}}} \right)}\right)}$$
=
/ / y \\ / / y \\
I*im|asin|------------|| + re|asin|------------||
| | _________|| | | _________||
| | / 2 2 || | | / 2 2 ||
\ \\/ x + y // \ \\/ x + y //
$$\operatorname{re}{\left(\operatorname{asin}{\left(\frac{y}{\sqrt{x^{2} + y^{2}}} \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(\frac{y}{\sqrt{x^{2} + y^{2}}} \right)}\right)}$$
product
/ / y \\ / / y \\
I*im|asin|------------|| + re|asin|------------||
| | _________|| | | _________||
| | / 2 2 || | | / 2 2 ||
\ \\/ x + y // \ \\/ x + y //
$$\operatorname{re}{\left(\operatorname{asin}{\left(\frac{y}{\sqrt{x^{2} + y^{2}}} \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(\frac{y}{\sqrt{x^{2} + y^{2}}} \right)}\right)}$$
=
/ / y \\ / / y \\
I*im|asin|------------|| + re|asin|------------||
| | _________|| | | _________||
| | / 2 2 || | | / 2 2 ||
\ \\/ x + y // \ \\/ x + y //
$$\operatorname{re}{\left(\operatorname{asin}{\left(\frac{y}{\sqrt{x^{2} + y^{2}}} \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(\frac{y}{\sqrt{x^{2} + y^{2}}} \right)}\right)}$$
i*im(asin(y/sqrt(x^2 + y^2))) + re(asin(y/sqrt(x^2 + y^2)))