Mister Exam
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How to use it?
- Equation:
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Equation 5*x^2=35*x
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Equation 10x-20=5x
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Equation x^2+4*x-32=0
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Equation 4*(x-6)=x-9
- Express {x} in terms of y where:
- 8*x-16*y=14
- 15*x-3*y=19
- 11*x+8*y=-16
- -11*x-1*y=12
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Identical expressions
- y*cosx+sinx= one
- y multiply by co sinus of e of x plus sinus of x equally 1
- y multiply by co sinus of e of x plus sinus of x equally one
- ycosx+sinx=1
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Similar expressions
- y*cosx-sinx=1
y*cosx+sinx=1 equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
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y*cos(x) + sin(x) = 1
$$y \cos{\left(x \right)} + \sin{\left(x \right)} = 1$$
The graph
Rapid solution
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pi
x1 = --
2
$$x_{1} = \frac{\pi}{2}$$
/ /-1 + y\\ / /-1 + y\\
x2 = - 2*re|atan|------|| - 2*I*im|atan|------||
\ \1 + y // \ \1 + y //
$$x_{2} = - 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{y - 1}{y + 1} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{y - 1}{y + 1} \right)}\right)}$$
x2 = -2*re(atan((y - 1)/(y + 1))) - 2*i*im(atan((y - 1)/(y + 1)))
Sum and product of roots
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sum
pi / /-1 + y\\ / /-1 + y\\ -- + - 2*re|atan|------|| - 2*I*im|atan|------|| 2 \ \1 + y // \ \1 + y //
$$\left(- 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{y - 1}{y + 1} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{y - 1}{y + 1} \right)}\right)}\right) + \frac{\pi}{2}$$
=
pi / /-1 + y\\ / /-1 + y\\ -- - 2*re|atan|------|| - 2*I*im|atan|------|| 2 \ \1 + y // \ \1 + y //
$$- 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{y - 1}{y + 1} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{y - 1}{y + 1} \right)}\right)} + \frac{\pi}{2}$$
product
pi / / /-1 + y\\ / /-1 + y\\\ --*|- 2*re|atan|------|| - 2*I*im|atan|------||| 2 \ \ \1 + y // \ \1 + y ///
$$\frac{\pi}{2} \left(- 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{y - 1}{y + 1} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{y - 1}{y + 1} \right)}\right)}\right)$$
=
/ / /-1 + y\\ / /-1 + y\\\
-pi*|I*im|atan|------|| + re|atan|------|||
\ \ \1 + y // \ \1 + y ///
$$- \pi \left(\operatorname{re}{\left(\operatorname{atan}{\left(\frac{y - 1}{y + 1} \right)}\right)} + i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{y - 1}{y + 1} \right)}\right)}\right)$$
-pi*(i*im(atan((-1 + y)/(1 + y))) + re(atan((-1 + y)/(1 + y))))