Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation 8*x-3*(2*x+1)=2*x+4
-
Equation 3*9^(x-1/2)-7*6^x+3*4^(x+1)=0
-
Equation 9x-26=30-5x
-
Equation x+19=12
- Express {x} in terms of y where:
- 12*x+14*y=-15
- -9*x-15*y=-4
- 12*x-14*y=20
- 11*x-20*y=-10
- Integral of d{x}:
-
sinx*sin5x
-
cos4x
- Derivative of:
-
cos4x
- Canonical form:
- cos4x
-
Identical expressions
- sinx*sin5x=cos4x
- sinus of x multiply by sinus of 5x equally co sinus of e of 4x
- sinxsin5x=cos4x
-
Similar expressions
- 60-80cos(4x/5)+20cos(8x/5)=0
- sinx*sin(5*x)=cos(4*x)
- sin(5*x)=cos(4*x)
- sqrt(sin^4x+1)+sqrt(cos^4x+1)=5
sinx*sin5x=cos4x equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
sin(x)*sin(5*x) = cos(4*x)
$$\sin{\left(x \right)} \sin{\left(5 x \right)} = \cos{\left(4 x \right)}$$
Sum and product of roots
[src]
sum
9*pi 7*pi pi 3*pi pi pi 3*pi pi 7*pi 9*pi - ---- - ---- - -- - ---- - -- + -- + ---- + -- + ---- + ---- 10 10 2 10 10 10 10 2 10 10
$$\left(\left(\left(\left(\left(\left(\left(\left(- \frac{9 \pi}{10} - \frac{7 \pi}{10}\right) - \frac{\pi}{2}\right) - \frac{3 \pi}{10}\right) - \frac{\pi}{10}\right) + \frac{\pi}{10}\right) + \frac{3 \pi}{10}\right) + \frac{\pi}{2}\right) + \frac{7 \pi}{10}\right) + \frac{9 \pi}{10}$$
=
0
$$0$$
product
-9*pi -7*pi -pi -3*pi -pi pi 3*pi pi 7*pi 9*pi -----*-----*----*-----*----*--*----*--*----*---- 10 10 2 10 10 10 10 2 10 10
$$\frac{9 \pi}{10} \frac{7 \pi}{10} \frac{\pi}{2} \frac{3 \pi}{10} \frac{\pi}{10} \cdot - \frac{\pi}{10} \cdot - \frac{3 \pi}{10} \cdot - \frac{\pi}{2} \cdot - \frac{9 \pi}{10} \left(- \frac{7 \pi}{10}\right)$$
=
10 -35721*pi ----------- 400000000
$$- \frac{35721 \pi^{10}}{400000000}$$
-35721*pi^10/400000000
Rapid solution
[src]
-9*pi
x1 = -----
10
$$x_{1} = - \frac{9 \pi}{10}$$
-7*pi
x2 = -----
10
$$x_{2} = - \frac{7 \pi}{10}$$
-pi
x3 = ----
2
$$x_{3} = - \frac{\pi}{2}$$
-3*pi
x4 = -----
10
$$x_{4} = - \frac{3 \pi}{10}$$
-pi
x5 = ----
10
$$x_{5} = - \frac{\pi}{10}$$
pi
x6 = --
10
$$x_{6} = \frac{\pi}{10}$$
3*pi
x7 = ----
10
$$x_{7} = \frac{3 \pi}{10}$$
pi
x8 = --
2
$$x_{8} = \frac{\pi}{2}$$
7*pi
x9 = ----
10
$$x_{9} = \frac{7 \pi}{10}$$
9*pi
x10 = ----
10
$$x_{10} = \frac{9 \pi}{10}$$
x10 = 9*pi/10
Numerical answer
[src]
x1 = 93.9336203423348
x2 = -61.8893752757189
x3 = 7.85398168446658
x4 = -48.0663675999238
x5 = 39.8982267005904
x6 = -63.7743308678728
x7 = 39.2699081498428
x8 = 60.0044196835651
x9 = 24.1902634326414
x10 = 83.8805238508475
x11 = 51.8362788222469
x12 = -70.0575161750524
x13 = -21.6769893097696
x14 = 16.0221225333079
x15 = -27.9601746169492
x16 = -31.7300858012569
x17 = -49.9513231920777
x18 = 68.1725605828985
x19 = 66.2876049907446
x20 = -9.73893722612836
x21 = 78.2256570743859
x22 = 27.9601746169492
x23 = -23.5619448943193
x24 = 22.3053078404875
x25 = 90.1637091580271
x26 = 12.2522113490002
x27 = -89.5353904622891
x28 = 70.0575161750524
x29 = 32.3584043319749
x30 = 2.19911485751286
x31 = -5.96902604182061
x32 = -77.5973385436679
x33 = 48.0663675999238
x34 = 26.0752190247953
x35 = 73.8274273864408
x36 = -60.0044196835651
x37 = -81.9955682586936
x38 = 4.08407044966673
x39 = 98.3318500573605
x40 = -4.08407044966673
x41 = 56.2345084992573
x42 = 44.2964564156161
x43 = -67.5442419493278
x44 = -80.1106126089377
x45 = -71.9424717672063
x46 = -36.1283154601932
x47 = 61.8893752757189
x48 = 88.2787535658732
x49 = -19.7920337176157
x50 = -55.6061899685393
x51 = -51.8362786978016
x52 = -14.1371668872424
x53 = 64.4026493525391
x54 = -7.85398154718208
x55 = -29.8451301142458
x56 = -87.6504350351552
x57 = -39.8982267005904
x58 = -75.712382951514
x59 = 58.7477826221291
x60 = -1.57079634217526
x61 = -93.9336203423348
x62 = -38.0132711084365
x63 = -73.827427283678
x64 = 54.3495529071034
x65 = 29.8451302545263
x66 = 100.216805649514
x67 = -16.0221225333079
x68 = 92.0486647501809
x69 = 71.9424717672063
x70 = -53.7212343763855
x71 = 34.2433599241287
x72 = -43.6681378848981
x73 = -41.7831822927443
x74 = 46.18141200777
x75 = -17.9070781254618
x76 = -95.8185758695698
x77 = 86.3937979237947
x78 = 0.314159265358979
x79 = 5.96902604182061
x80 = 95.8185759450348
x81 = 38.0132711084365
x82 = -83.8805238508475
x83 = -97.7035315266426
x84 = 42.4115007836476
x85 = 20.4203522181614
x86 = 10.3672557568463
x87 = 76.340701482232
x88 = -45.5530934328517
x89 = -65.6592864600267
x90 = -11.6238928182822
x91 = -92.0486647501809
x92 = 81.9955682586936
x93 = -26.0752190247953
x94 = -85.7654794430014
x95 = 17.9070781254618
x96 = -58.1194640341413
x97 = 49.9513231920777
x98 = -33.6150413934108
x98 = -33.6150413934108