Mister Exam
Other calculators
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How to use it?
- Equation:
- Equation x+y=5
-
Equation x^2+5x+6=0
-
Equation 2x^2-18=0
-
Equation x^6=64
- Express {x} in terms of y where:
- 10*x-18*y=3
- -14*x-12*y=5
- 13*x-12*y=19
- 3*x-7*y=13
- Derivative of:
-
sin(t)
- Limit of the function:
-
sin(t)
- -sqrt(3)
- Integral of d{x}:
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sin(t)
-
Identical expressions
- sin(t)=-sqrt(three)
- sinus of (t) equally minus square root of (3)
- sinus of (t) equally minus square root of (three)
- sin(t)=-√(3)
- sint=-sqrt3
-
Similar expressions
- (26+15sqrt3)^x-5(7+4sqrt3)^x+6(2+sqrt3)^x+(2-sqrt3)^x=5
- sint-2sintcost-cost+1=0
- sin(t)=+sqrt(3)
sin(t)=-sqrt(3) equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$\sin{\left(t \right)} = - \sqrt{3}$$
- this is the simplest trigonometric equation
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.
$$\sin{\left(t \right)} = - \sqrt{3}$$
- this is the simplest trigonometric equation
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]
/ / ___\\ / / ___\\ t1 = pi + I*im\asin\\/ 3 // + re\asin\\/ 3 //
$$t_{1} = \operatorname{re}{\left(\operatorname{asin}{\left(\sqrt{3} \right)}\right)} + \pi + i \operatorname{im}{\left(\operatorname{asin}{\left(\sqrt{3} \right)}\right)}$$
/ / ___\\ / / ___\\ t2 = - re\asin\\/ 3 // - I*im\asin\\/ 3 //
$$t_{2} = - \operatorname{re}{\left(\operatorname{asin}{\left(\sqrt{3} \right)}\right)} - i \operatorname{im}{\left(\operatorname{asin}{\left(\sqrt{3} \right)}\right)}$$
t2 = -re(asin(sqrt(3))) - i*im(asin(sqrt(3)))
Sum and product of roots
[src]
sum
/ / ___\\ / / ___\\ / / ___\\ / / ___\\ pi + I*im\asin\\/ 3 // + re\asin\\/ 3 // + - re\asin\\/ 3 // - I*im\asin\\/ 3 //
$$\left(\operatorname{re}{\left(\operatorname{asin}{\left(\sqrt{3} \right)}\right)} + \pi + i \operatorname{im}{\left(\operatorname{asin}{\left(\sqrt{3} \right)}\right)}\right) + \left(- \operatorname{re}{\left(\operatorname{asin}{\left(\sqrt{3} \right)}\right)} - i \operatorname{im}{\left(\operatorname{asin}{\left(\sqrt{3} \right)}\right)}\right)$$
=
pi
$$\pi$$
product
/ / / ___\\ / / ___\\\ / / / ___\\ / / ___\\\ \pi + I*im\asin\\/ 3 // + re\asin\\/ 3 ///*\- re\asin\\/ 3 // - I*im\asin\\/ 3 ///
$$\left(- \operatorname{re}{\left(\operatorname{asin}{\left(\sqrt{3} \right)}\right)} - i \operatorname{im}{\left(\operatorname{asin}{\left(\sqrt{3} \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{asin}{\left(\sqrt{3} \right)}\right)} + \pi + i \operatorname{im}{\left(\operatorname{asin}{\left(\sqrt{3} \right)}\right)}\right)$$
=
/ / / ___\\ / / ___\\\ / / / ___\\ / / ___\\\ -\I*im\asin\\/ 3 // + re\asin\\/ 3 ///*\pi + I*im\asin\\/ 3 // + re\asin\\/ 3 ///
$$- \left(\operatorname{re}{\left(\operatorname{asin}{\left(\sqrt{3} \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(\sqrt{3} \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{asin}{\left(\sqrt{3} \right)}\right)} + \pi + i \operatorname{im}{\left(\operatorname{asin}{\left(\sqrt{3} \right)}\right)}\right)$$
-(i*im(asin(sqrt(3))) + re(asin(sqrt(3))))*(pi + i*im(asin(sqrt(3))) + re(asin(sqrt(3))))
Numerical answer
[src]
t1 = 4.71238898038469 - 1.14621583478059*i
t2 = -1.5707963267949 + 1.14621583478059*i
t2 = -1.5707963267949 + 1.14621583478059*i