Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation x^2-3x+1=0
-
Equation 2*sin(x)=1
-
Equation -20+2x=18
-
Equation x^4-2*x^3+x^2-1=0
- Express {x} in terms of y where:
- 1*x+6*y=-6
- -5*x-2*y=9
- 1*x+11*y=-3
- 10*x-6*y=9
- Derivative of:
- sqrt(2)
- Integral of d{x}:
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sqrt(2)
- sqrt(2)
-
Identical expressions
- sin((pi(x- three))/ four)=sqrt(two)
- sinus of (( Pi (x minus 3)) divide by 4) equally square root of (2)
- sinus of (( Pi (x minus three)) divide by four) equally square root of (two)
- sin((pi(x-3))/4)=√(2)
- sinpix-3/4=sqrt2
- sin((pi(x-3)) divide by 4)=sqrt(2)
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Similar expressions
- cos^2(x)-sqrt2cos(x)-2sin(2x)-cos^2(2x)+2,5=0
- sin((pi(x+3))/4)=sqrt(2)
- (sinx-sin2x)/sqrt(2cosx-1)=0
sin((pi(x-3))/4)=sqrt(2) equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
/pi*(x - 3)\ ___ sin|----------| = \/ 2 \ 4 /
$$\sin{\left(\frac{\pi \left(x - 3\right)}{4} \right)} = \sqrt{2}$$
Detail solution
Given the equation
$$\sin{\left(\frac{\pi \left(x - 3\right)}{4} \right)} = \sqrt{2}$$
- this is the simplest trigonometric equation
The equation is transformed to
$$\sin{\left(\frac{\pi x}{4} + \frac{\pi}{4} \right)} = - \sqrt{2}$$
As right part of the equation
modulo =
but sin
can no be more than 1 or less than -1
so the solution of the equation d'not exist.
$$\sin{\left(\frac{\pi \left(x - 3\right)}{4} \right)} = \sqrt{2}$$
- this is the simplest trigonometric equation
Divide both parts of the equation by -1
The equation is transformed to
$$\sin{\left(\frac{\pi x}{4} + \frac{\pi}{4} \right)} = - \sqrt{2}$$
As right part of the equation
modulo =
True
but sin
can no be more than 1 or less than -1
so the solution of the equation d'not exist.
Rapid solution
[src]
/ / ___\\ / / ___\\
pi + 4*re\asin\\/ 2 // 4*I*im\asin\\/ 2 //
x1 = - ---------------------- - -------------------
pi pi
$$x_{1} = - \frac{\pi + 4 \operatorname{re}{\left(\operatorname{asin}{\left(\sqrt{2} \right)}\right)}}{\pi} - \frac{4 i \operatorname{im}{\left(\operatorname{asin}{\left(\sqrt{2} \right)}\right)}}{\pi}$$
/ / ___\\ / / ___\\
4*re\asin\\/ 2 // 4*I*im\asin\\/ 2 //
x2 = 3 + ----------------- + -------------------
pi pi
$$x_{2} = \frac{4 \operatorname{re}{\left(\operatorname{asin}{\left(\sqrt{2} \right)}\right)}}{\pi} + 3 + \frac{4 i \operatorname{im}{\left(\operatorname{asin}{\left(\sqrt{2} \right)}\right)}}{\pi}$$
x2 = 4*re(asin(sqrt(2)))/pi + 3 + 4*i*im(asin(sqrt(2)))/pi
Sum and product of roots
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sum
/ / ___\\ / / ___\\ / / ___\\ / / ___\\
pi + 4*re\asin\\/ 2 // 4*I*im\asin\\/ 2 // 4*re\asin\\/ 2 // 4*I*im\asin\\/ 2 //
- ---------------------- - ------------------- + 3 + ----------------- + -------------------
pi pi pi pi
$$\left(\frac{4 \operatorname{re}{\left(\operatorname{asin}{\left(\sqrt{2} \right)}\right)}}{\pi} + 3 + \frac{4 i \operatorname{im}{\left(\operatorname{asin}{\left(\sqrt{2} \right)}\right)}}{\pi}\right) + \left(- \frac{\pi + 4 \operatorname{re}{\left(\operatorname{asin}{\left(\sqrt{2} \right)}\right)}}{\pi} - \frac{4 i \operatorname{im}{\left(\operatorname{asin}{\left(\sqrt{2} \right)}\right)}}{\pi}\right)$$
=
/ / ___\\ / / ___\\
pi + 4*re\asin\\/ 2 // 4*re\asin\\/ 2 //
3 - ---------------------- + -----------------
pi pi
$$- \frac{\pi + 4 \operatorname{re}{\left(\operatorname{asin}{\left(\sqrt{2} \right)}\right)}}{\pi} + \frac{4 \operatorname{re}{\left(\operatorname{asin}{\left(\sqrt{2} \right)}\right)}}{\pi} + 3$$
product
/ / / ___\\ / / ___\\\ / / / ___\\ / / ___\\\ | pi + 4*re\asin\\/ 2 // 4*I*im\asin\\/ 2 //| | 4*re\asin\\/ 2 // 4*I*im\asin\\/ 2 //| |- ---------------------- - -------------------|*|3 + ----------------- + -------------------| \ pi pi / \ pi pi /
$$\left(- \frac{\pi + 4 \operatorname{re}{\left(\operatorname{asin}{\left(\sqrt{2} \right)}\right)}}{\pi} - \frac{4 i \operatorname{im}{\left(\operatorname{asin}{\left(\sqrt{2} \right)}\right)}}{\pi}\right) \left(\frac{4 \operatorname{re}{\left(\operatorname{asin}{\left(\sqrt{2} \right)}\right)}}{\pi} + 3 + \frac{4 i \operatorname{im}{\left(\operatorname{asin}{\left(\sqrt{2} \right)}\right)}}{\pi}\right)$$
=
/ / / ___\\ / / ___\\\ / / / ___\\ / / ___\\\
-\pi + 4*re\asin\\/ 2 // + 4*I*im\asin\\/ 2 ///*\3*pi + 4*re\asin\\/ 2 // + 4*I*im\asin\\/ 2 ///
-------------------------------------------------------------------------------------------------
2
pi
$$- \frac{\left(\pi + 4 \operatorname{re}{\left(\operatorname{asin}{\left(\sqrt{2} \right)}\right)} + 4 i \operatorname{im}{\left(\operatorname{asin}{\left(\sqrt{2} \right)}\right)}\right) \left(4 \operatorname{re}{\left(\operatorname{asin}{\left(\sqrt{2} \right)}\right)} + 3 \pi + 4 i \operatorname{im}{\left(\operatorname{asin}{\left(\sqrt{2} \right)}\right)}\right)}{\pi^{2}}$$
-(pi + 4*re(asin(sqrt(2))) + 4*i*im(asin(sqrt(2))))*(3*pi + 4*re(asin(sqrt(2))) + 4*i*im(asin(sqrt(2))))/pi^2
Numerical answer
[src]
x1 = -3.0 + 1.12219970467836*i
x2 = 5.0 - 1.12219970467836*i
x2 = 5.0 - 1.12219970467836*i