Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation 14/(x-3)=-7/9
-
Equation x^4+2*x^2-8=0
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Equation 9x−9(x+1)=−2x
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Equation x^4+4=0
- Express {x} in terms of y where:
- -17*x+1*y=-11
- 1*x+4*y=20
- -18*x-2*y=9
- -20*x-14*y=5
- Sum of series:
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1/2
- Integral of d{x}:
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1/2
- Derivative of:
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1/2
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Identical expressions
- sinpi(five *x+ fifteen)/ six = one / two
- sinus of Pi (5 multiply by x plus 15) divide by 6 equally 1 divide by 2
- sinus of Pi (five multiply by x plus fifteen) divide by six equally one divide by two
- sinpi(5x+15)/6=1/2
- sinpi5x+15/6=1/2
- sinpi(5*x+15) divide by 6=1 divide by 2
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Similar expressions
- sinpi(5*x-15)/6=1/2
- (x-1)/(2x+3)-(2x-1)/(3-2x)=0
sinpi(5*x+15)/6=1/2 equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
sin(p)*I*(5*x + 15)
------------------- = 1/2
6
$$\frac{i \sin{\left(p \right)} \left(5 x + 15\right)}{6} = \frac{1}{2}$$
Detail solution
Given the equation
$$\frac{i \sin{\left(p \right)} \left(5 x + 15\right)}{6} = \frac{1}{2}$$
transform
$$\frac{5 i \left(x + 3\right) \sin{\left(p \right)}}{6} - \frac{3}{2} = 0$$
$$\frac{i \sin{\left(p \right)} \left(5 x + 15\right)}{6} - \frac{3}{2} = 0$$
Do replacement
$$w = \sin{\left(p \right)}$$
Expand brackets in the left part
Looking for similar summands in the left part:
Move free summands (without w)
from left part to right part, we given:
$$\frac{i w \left(5 x + 15\right)}{6} = \frac{3}{2}$$
Divide both parts of the equation by i*(15 + 5*x)/6
We get the answer: w = -9*i/(15 + 5*x)
do backward replacement
$$\sin{\left(p \right)} = w$$
substitute w:
$$\frac{i \sin{\left(p \right)} \left(5 x + 15\right)}{6} = \frac{1}{2}$$
transform
$$\frac{5 i \left(x + 3\right) \sin{\left(p \right)}}{6} - \frac{3}{2} = 0$$
$$\frac{i \sin{\left(p \right)} \left(5 x + 15\right)}{6} - \frac{3}{2} = 0$$
Do replacement
$$w = \sin{\left(p \right)}$$
Expand brackets in the left part
-3/2 + i*w5*x/6+15/6 = 0
Looking for similar summands in the left part:
-3/2 + i*w*(15 + 5*x)/6 = 0
Move free summands (without w)
from left part to right part, we given:
$$\frac{i w \left(5 x + 15\right)}{6} = \frac{3}{2}$$
Divide both parts of the equation by i*(15 + 5*x)/6
w = 3/2 / (i*(15 + 5*x)/6)
We get the answer: w = -9*i/(15 + 5*x)
do backward replacement
$$\sin{\left(p \right)} = w$$
substitute w:
The graph
Rapid solution
[src]
3*cos(re(p))*sinh(im(p)) 3*I*cosh(im(p))*sin(re(p))
x1 = -3 - ------------------------------------------------------- - -------------------------------------------------------
/ 2 2 2 2 \ / 2 2 2 2 \
5*\cos (re(p))*sinh (im(p)) + cosh (im(p))*sin (re(p))/ 5*\cos (re(p))*sinh (im(p)) + cosh (im(p))*sin (re(p))/
$$x_{1} = -3 - \frac{3 i \sin{\left(\operatorname{re}{\left(p\right)} \right)} \cosh{\left(\operatorname{im}{\left(p\right)} \right)}}{5 \left(\sin^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(p\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(p\right)} \right)}\right)} - \frac{3 \cos{\left(\operatorname{re}{\left(p\right)} \right)} \sinh{\left(\operatorname{im}{\left(p\right)} \right)}}{5 \left(\sin^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(p\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(p\right)} \right)}\right)}$$
x1 = -3 - 3*i*sin(re(p))*cosh(im(p))/(5*(sin(re(p))^2*cosh(im(p))^2 + cos(re(p))^2*sinh(im(p))^2)) - 3*cos(re(p))*sinh(im(p))/(5*(sin(re(p))^2*cosh(im(p))^2 + cos(re(p))^2*sinh(im(p))^2))
Sum and product of roots
[src]
sum
3*cos(re(p))*sinh(im(p)) 3*I*cosh(im(p))*sin(re(p))
-3 - ------------------------------------------------------- - -------------------------------------------------------
/ 2 2 2 2 \ / 2 2 2 2 \
5*\cos (re(p))*sinh (im(p)) + cosh (im(p))*sin (re(p))/ 5*\cos (re(p))*sinh (im(p)) + cosh (im(p))*sin (re(p))/
$$-3 - \frac{3 i \sin{\left(\operatorname{re}{\left(p\right)} \right)} \cosh{\left(\operatorname{im}{\left(p\right)} \right)}}{5 \left(\sin^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(p\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(p\right)} \right)}\right)} - \frac{3 \cos{\left(\operatorname{re}{\left(p\right)} \right)} \sinh{\left(\operatorname{im}{\left(p\right)} \right)}}{5 \left(\sin^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(p\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(p\right)} \right)}\right)}$$
=
3*cos(re(p))*sinh(im(p)) 3*I*cosh(im(p))*sin(re(p))
-3 - ------------------------------------------------------- - -------------------------------------------------------
/ 2 2 2 2 \ / 2 2 2 2 \
5*\cos (re(p))*sinh (im(p)) + cosh (im(p))*sin (re(p))/ 5*\cos (re(p))*sinh (im(p)) + cosh (im(p))*sin (re(p))/
$$-3 - \frac{3 i \sin{\left(\operatorname{re}{\left(p\right)} \right)} \cosh{\left(\operatorname{im}{\left(p\right)} \right)}}{5 \left(\sin^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(p\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(p\right)} \right)}\right)} - \frac{3 \cos{\left(\operatorname{re}{\left(p\right)} \right)} \sinh{\left(\operatorname{im}{\left(p\right)} \right)}}{5 \left(\sin^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(p\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(p\right)} \right)}\right)}$$
product
3*cos(re(p))*sinh(im(p)) 3*I*cosh(im(p))*sin(re(p))
-3 - ------------------------------------------------------- - -------------------------------------------------------
/ 2 2 2 2 \ / 2 2 2 2 \
5*\cos (re(p))*sinh (im(p)) + cosh (im(p))*sin (re(p))/ 5*\cos (re(p))*sinh (im(p)) + cosh (im(p))*sin (re(p))/
$$-3 - \frac{3 i \sin{\left(\operatorname{re}{\left(p\right)} \right)} \cosh{\left(\operatorname{im}{\left(p\right)} \right)}}{5 \left(\sin^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(p\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(p\right)} \right)}\right)} - \frac{3 \cos{\left(\operatorname{re}{\left(p\right)} \right)} \sinh{\left(\operatorname{im}{\left(p\right)} \right)}}{5 \left(\sin^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(p\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(p\right)} \right)}\right)}$$
=
-(I*(3/5 + 3*cos(re(p))*sinh(im(p))) + 3*cosh(im(p))*sin(re(p)))
-----------------------------------------------------------------
cosh(im(p))*sin(re(p)) + I*cos(re(p))*sinh(im(p))
$$- \frac{i \left(3 \cos{\left(\operatorname{re}{\left(p\right)} \right)} \sinh{\left(\operatorname{im}{\left(p\right)} \right)} + \frac{3}{5}\right) + 3 \sin{\left(\operatorname{re}{\left(p\right)} \right)} \cosh{\left(\operatorname{im}{\left(p\right)} \right)}}{\sin{\left(\operatorname{re}{\left(p\right)} \right)} \cosh{\left(\operatorname{im}{\left(p\right)} \right)} + i \cos{\left(\operatorname{re}{\left(p\right)} \right)} \sinh{\left(\operatorname{im}{\left(p\right)} \right)}}$$
-(i*(3/5 + 3*cos(re(p))*sinh(im(p))) + 3*cosh(im(p))*sin(re(p)))/(cosh(im(p))*sin(re(p)) + i*cos(re(p))*sinh(im(p)))