Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation 1-7(4+2x)=-9-4x
-
Equation tan(x)=-1
-
Equation x^2+8x+7=0
-
Equation 2*x=0
- Express {x} in terms of y where:
- 4*x+15*y=19
- 4*x-13*y=13
- 4*x-15*y=19
- 17*x-18*y=10
-
Identical expressions
- five *sin^2x+ twenty-one *sinx+ four = zero
- 5 multiply by sinus of squared x plus 21 multiply by sinus of x plus 4 equally 0
- five multiply by sinus of squared x plus twenty minus one multiply by sinus of x plus four equally zero
- 5*sin2x+21*sinx+4=0
- 5*sin²x+21*sinx+4=0
- 5*sin to the power of 2x+21*sinx+4=0
- 5sin^2x+21sinx+4=0
- 5sin2x+21sinx+4=0
- 5*sin^2x+21*sinx+4=O
-
Similar expressions
- 5*sin^2x-21*sinx+4=0
- 5*sin^2x+21*sinx-4=0
5*sin^2x+21*sinx+4=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
2 5*sin (x) + 21*sin(x) + 4 = 0
$$5 \sin^{2}{\left(x \right)} + 21 \sin{\left(x \right)} + 4 = 0$$
Detail solution
Given the equation:
$$5 \sin^{2}{\left(x \right)} + 21 \sin{\left(x \right)} + 4 = 0$$
Transform
$$5 \sin^{2}{\left(x \right)} + 21 \sin{\left(x \right)} + 4 = 0$$
$$\left(\sin{\left(x \right)} + 4\right) \left(5 \sin{\left(x \right)} + 1\right) = 0$$
Consider each factor separately
$$5 \sin{\left(x \right)} + 1 = 0$$
- this is the simplest trigonometric equation
Move $1$ to right part of the equation
with the change of sign in $1$
We get:
$$5 \sin{\left(x \right)} = -1$$
Divide both parts of the equation by $5$
The equation is transformed to
$$\sin{\left(x \right)} = - \frac{1}{5}$$
This equation is transformed to
$$x = 2 \pi n + \operatorname{asin}{\left(- \frac{1}{5} \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(- \frac{1}{5} \right)} + \pi$$
Or
$$x = 2 \pi n - \operatorname{asin}{\left(\frac{1}{5} \right)}$$
$$x = 2 \pi n + \operatorname{asin}{\left(\frac{1}{5} \right)} + \pi$$
, where n - is a integer
$$\sin{\left(x \right)} + 4 = 0$$
- this is the simplest trigonometric equation
Move $4$ to right part of the equation
with the change of sign in $4$
We get:
$$\sin{\left(x \right)} = -4$$
As right part of the equation
modulo =
$$4 > 1$$
but sin can no be more than 1 or less than -1
so the solution of the equation d'not exist.
The final answer:
$$x_{1} = 2 \pi n - \operatorname{asin}{\left(\frac{1}{5} \right)}$$
$$x_{2} = 2 \pi n + \operatorname{asin}{\left(\frac{1}{5} \right)} + \pi$$
$$5 \sin^{2}{\left(x \right)} + 21 \sin{\left(x \right)} + 4 = 0$$
Transform
$$5 \sin^{2}{\left(x \right)} + 21 \sin{\left(x \right)} + 4 = 0$$
$$\left(\sin{\left(x \right)} + 4\right) \left(5 \sin{\left(x \right)} + 1\right) = 0$$
Consider each factor separately
Step
$$5 \sin{\left(x \right)} + 1 = 0$$
- this is the simplest trigonometric equation
Move $1$ to right part of the equation
with the change of sign in $1$
We get:
$$5 \sin{\left(x \right)} = -1$$
Divide both parts of the equation by $5$
The equation is transformed to
$$\sin{\left(x \right)} = - \frac{1}{5}$$
This equation is transformed to
$$x = 2 \pi n + \operatorname{asin}{\left(- \frac{1}{5} \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(- \frac{1}{5} \right)} + \pi$$
Or
$$x = 2 \pi n - \operatorname{asin}{\left(\frac{1}{5} \right)}$$
$$x = 2 \pi n + \operatorname{asin}{\left(\frac{1}{5} \right)} + \pi$$
, where n - is a integer
Step
$$\sin{\left(x \right)} + 4 = 0$$
- this is the simplest trigonometric equation
Move $4$ to right part of the equation
with the change of sign in $4$
We get:
$$\sin{\left(x \right)} = -4$$
As right part of the equation
modulo =
$$4 > 1$$
but sin can no be more than 1 or less than -1
so the solution of the equation d'not exist.
The final answer:
$$x_{1} = 2 \pi n - \operatorname{asin}{\left(\frac{1}{5} \right)}$$
$$x_{2} = 2 \pi n + \operatorname{asin}{\left(\frac{1}{5} \right)} + \pi$$
Rapid solution
[src]
x_1 = pi + asin(1/5)
$$x_{1} = \operatorname{asin}{\left(\frac{1}{5} \right)} + \pi$$
x_2 = -asin(1/5)
$$x_{2} = - \operatorname{asin}{\left(\frac{1}{5} \right)}$$
x_3 = pi + I*im(asin(4)) + re(asin(4))
$$x_{3} = \operatorname{re}{\left(\operatorname{asin}{\left(4 \right)}\right)} + \pi + i \operatorname{im}{\left(\operatorname{asin}{\left(4 \right)}\right)}$$
x_4 = -re(asin(4)) - I*im(asin(4))
$$x_{4} = - \operatorname{re}{\left(\operatorname{asin}{\left(4 \right)}\right)} - i \operatorname{im}{\left(\operatorname{asin}{\left(4 \right)}\right)}$$
Sum and product of roots
[src]
sum
pi + asin(1/5) + -asin(1/5) + pi + I*im(asin(4)) + re(asin(4)) + -re(asin(4)) - I*im(asin(4))
$$\left(\operatorname{asin}{\left(\frac{1}{5} \right)} + \pi\right) + \left(- \operatorname{asin}{\left(\frac{1}{5} \right)}\right) + \left(\operatorname{re}{\left(\operatorname{asin}{\left(4 \right)}\right)} + \pi + i \operatorname{im}{\left(\operatorname{asin}{\left(4 \right)}\right)}\right) + \left(- \operatorname{re}{\left(\operatorname{asin}{\left(4 \right)}\right)} - i \operatorname{im}{\left(\operatorname{asin}{\left(4 \right)}\right)}\right)$$
=
2*pi
$$2 \pi$$
product
pi + asin(1/5) * -asin(1/5) * pi + I*im(asin(4)) + re(asin(4)) * -re(asin(4)) - I*im(asin(4))
$$\left(\operatorname{asin}{\left(\frac{1}{5} \right)} + \pi\right) * \left(- \operatorname{asin}{\left(\frac{1}{5} \right)}\right) * \left(\operatorname{re}{\left(\operatorname{asin}{\left(4 \right)}\right)} + \pi + i \operatorname{im}{\left(\operatorname{asin}{\left(4 \right)}\right)}\right) * \left(- \operatorname{re}{\left(\operatorname{asin}{\left(4 \right)}\right)} - i \operatorname{im}{\left(\operatorname{asin}{\left(4 \right)}\right)}\right)$$
=
(pi + asin(1/5))*(I*im(asin(4)) + re(asin(4)))*(pi + I*im(asin(4)) + re(asin(4)))*asin(1/5)
$$\left(\operatorname{re}{\left(\operatorname{asin}{\left(4 \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(4 \right)}\right)}\right) \left(\operatorname{asin}{\left(\frac{1}{5} \right)} + \pi\right) \left(\operatorname{re}{\left(\operatorname{asin}{\left(4 \right)}\right)} + \pi + i \operatorname{im}{\left(\operatorname{asin}{\left(4 \right)}\right)}\right) \operatorname{asin}{\left(\frac{1}{5} \right)}$$
Numerical answer
[src]
x1 = 15.9093211887393
x2 = -34.3561612686974
x3 = 68.9136804581851
x4 = -50.466840378227
x5 = 85.0243595677148
x6 = -53.2057171902362
x7 = -63.0332109925862
x8 = -0.201357920790331
x9 = 34.7588771102781
x10 = -40.639346575877
x11 = 66.174803646176
x12 = 28.4756918030985
x13 = -69.3163962997658
x14 = 100.329606994083
x15 = 56.3473098438259
x16 = 94.0464216869035
x17 = 91.3075448748943
x18 = 53.6084330318168
x19 = -163.56417590746
x20 = -15.5066053471586
x21 = -84.6216437261341
x22 = -37.9004697638678
x23 = -88.1659522213045
x24 = 31.2145686151076
x25 = 9.62613588155971
x26 = -81.882766914125
x27 = 87.7632363797239
x28 = -78.3384584189545
x29 = -25.3340991495087
x30 = -9.22342003997905
x31 = 12.3650126935688
x32 = 41.0420624174576
x33 = -72.0552731117749
x34 = -12.7677285351495
x35 = 18.6481980007484
x36 = -13788.2487986848
x37 = -44.1836550710474
x38 = -90.9048290333137
x39 = -46.9225318830566
x40 = -31.6172844566883
x41 = -97.1880143404933
x42 = 72.4579889533556
x43 = -19.0509138423291
x44 = 37.4977539222872
x45 = 97.5907301820739
x46 = 6.08182738638926
x47 = -6.48454322796992
x48 = 59.8916183389964
x49 = 81.4800510725443
x50 = -2.94023473279946
x51 = 24.931383307928
x52 = -65.7720878045953
x53 = -21.7897906543382
x54 = 75.1968657653647
x55 = -94.4491375284841
x56 = 22.1925064959189
x57 = 62.6304951510055
x58 = -56.7500256854066
x59 = -358.342920430027
x60 = 348.918142469257
x61 = -59.4889024974157
x62 = 3.34295057438012
x63 = 43.7809392294668
x64 = 50.0641245366464
x65 = 47.3252477246372
x66 = -28.0729759615178
x67 = -75.5995816069454
x68 = 78.7411742605352
x69 = -100.732322835664
x69 = -100.732322835664
The graph