Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation sin(6*x)=9/8
- Equation (x^2-16)^2+(x^2-5x-36)^2=0
-
Equation (333+y)-1346=52471
-
Equation 43+x=500÷10
- Express {x} in terms of y where:
- 15*x-15*y=16
- 9*x+18*y=6
- (x^2+y^2-1)^3+x^2*y^3=0
- -1*x-19*y=-10
- Derivative of:
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sin(6*x)
- Graphing y =:
- sin(6*x)
- Integral of d{x}:
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sin(6*x)
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Identical expressions
- sin(six *x)= nine / eight
- sinus of (6 multiply by x) equally 9 divide by 8
- sinus of (six multiply by x) equally nine divide by eight
- sin(6x)=9/8
- sin6x=9/8
- sin(6*x)=9 divide by 8
-
Similar expressions
- sin6x+√3cos6x=-2cos8x.
- sin(6x)-cos(3x)=0
- sin(6*x-pi/6)=1/2
- (x-19)/8=1
sin(6*x)=9/8 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$\sin{\left(6 x \right)} = \frac{9}{8}$$
- 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.
$$\sin{\left(6 x \right)} = \frac{9}{8}$$
- 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]
re(asin(9/8)) pi I*im(asin(9/8))
x1 = - ------------- + -- - ---------------
6 6 6
$$x_{1} = - \frac{\operatorname{re}{\left(\operatorname{asin}{\left(\frac{9}{8} \right)}\right)}}{6} + \frac{\pi}{6} - \frac{i \operatorname{im}{\left(\operatorname{asin}{\left(\frac{9}{8} \right)}\right)}}{6}$$
re(asin(9/8)) I*im(asin(9/8))
x2 = ------------- + ---------------
6 6
$$x_{2} = \frac{\operatorname{re}{\left(\operatorname{asin}{\left(\frac{9}{8} \right)}\right)}}{6} + \frac{i \operatorname{im}{\left(\operatorname{asin}{\left(\frac{9}{8} \right)}\right)}}{6}$$
Sum and product of roots
[src]
sum
re(asin(9/8)) pi I*im(asin(9/8)) re(asin(9/8)) I*im(asin(9/8))
0 + - ------------- + -- - --------------- + ------------- + ---------------
6 6 6 6 6
$$\left(\frac{\operatorname{re}{\left(\operatorname{asin}{\left(\frac{9}{8} \right)}\right)}}{6} + \frac{i \operatorname{im}{\left(\operatorname{asin}{\left(\frac{9}{8} \right)}\right)}}{6}\right) - \left(- \frac{\pi}{6} + \frac{\operatorname{re}{\left(\operatorname{asin}{\left(\frac{9}{8} \right)}\right)}}{6} + \frac{i \operatorname{im}{\left(\operatorname{asin}{\left(\frac{9}{8} \right)}\right)}}{6}\right)$$
=
pi -- 6
$$\frac{\pi}{6}$$
product
/ re(asin(9/8)) pi I*im(asin(9/8))\ /re(asin(9/8)) I*im(asin(9/8))\ 1*|- ------------- + -- - ---------------|*|------------- + ---------------| \ 6 6 6 / \ 6 6 /
$$\left(\frac{\operatorname{re}{\left(\operatorname{asin}{\left(\frac{9}{8} \right)}\right)}}{6} + \frac{i \operatorname{im}{\left(\operatorname{asin}{\left(\frac{9}{8} \right)}\right)}}{6}\right) 1 \left(- \frac{\operatorname{re}{\left(\operatorname{asin}{\left(\frac{9}{8} \right)}\right)}}{6} + \frac{\pi}{6} - \frac{i \operatorname{im}{\left(\operatorname{asin}{\left(\frac{9}{8} \right)}\right)}}{6}\right)$$
=
-(I*im(asin(9/8)) + re(asin(9/8)))*(-pi + I*im(asin(9/8)) + re(asin(9/8)))
---------------------------------------------------------------------------
36
$$- \frac{\left(\operatorname{re}{\left(\operatorname{asin}{\left(\frac{9}{8} \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(\frac{9}{8} \right)}\right)}\right) \left(- \pi + \operatorname{re}{\left(\operatorname{asin}{\left(\frac{9}{8} \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(\frac{9}{8} \right)}\right)}\right)}{36}$$
-(i*im(asin(9/8)) + re(asin(9/8)))*(-pi + i*im(asin(9/8)) + re(asin(9/8)))/36
Numerical answer
[src]
x1 = 0.261799387799149 + 0.0824888205157545*i
x2 = 0.261799387799149 - 0.0824888205157545*i
x2 = 0.261799387799149 - 0.0824888205157545*i
The graph