Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation tgx=-(3/4)
-
Equation tgx=3/2
- Equation cos(3x)sin(3x)=cos(Pi/3)*cos(12x-3Pi/2)
- Equation tg(x)(ctg(x)-cos(x))=2sin(2x)^2
- 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
-
Identical expressions
- cos(three x)sin(3x)=cos(Pi/3)*cos(1 two x-3Pi/2)
- co sinus of e of (3x) sinus of (3x) equally co sinus of e of (Pi divide by 3) multiply by co sinus of e of (12x minus 3Pi divide by 2)
- co sinus of e of (three x) sinus of (3x) equally co sinus of e of (Pi divide by 3) multiply by co sinus of e of (1 two x minus 3Pi divide by 2)
- cos(3x)sin(3x)=cos(Pi/3)cos(12x-3Pi/2)
- cos3xsin3x=cosPi/3cos12x-3Pi/2
- cos(3x)sin(3x)=cos(Pi divide by 3)*cos(12x-3Pi divide by 2)
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Similar expressions
- cos(3x)sin(3x)=cos(Pi/3)*cos(12x+3Pi/2)
- cos(3*x)*sin(3*x)=1/2*sin(12*x)
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What you mean?
- sin(3*x)*cos(3*x) = cos((12*x - 3*pi)/2)*cos(pi/3)
- sin(3*x)*cos(3*x) = cos(12*(x - 3*pi)/2)*cos(pi/3)
- sin(3*x)*cos(3*x) = cos(pi/3)*cos(12*x - 3*pi/2)
- sin(3*x)*cos(3*x) = cos(pi/3)*cos(12*x - 3*pi/2)
You entered:
cos(3x)sin(3x)=cos(Pi/3)*cos(12x-3Pi/2)
What you mean?
cos(3x)sin(3x)=cos(Pi/3)*cos(12x-3Pi/2) equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
/pi\ / 3*pi\
cos(3*x)*sin(3*x) = cos|--|*cos|12*x - ----|
\3 / \ 2 /
$$\sin{\left(3 x \right)} \cos{\left(3 x \right)} = \cos{\left(\frac{\pi}{3} \right)} \cos{\left(12 x - \frac{3 \pi}{2} \right)}$$
Rapid solution
[src]
x1 = 0
$$x_{1} = 0$$
-11*pi
x2 = ------
6
$$x_{2} = - \frac{11 \pi}{6}$$
-5*pi
x3 = -----
3
$$x_{3} = - \frac{5 \pi}{3}$$
-3*pi
x4 = -----
2
$$x_{4} = - \frac{3 \pi}{2}$$
-4*pi
x5 = -----
3
$$x_{5} = - \frac{4 \pi}{3}$$
-7*pi
x6 = -----
6
$$x_{6} = - \frac{7 \pi}{6}$$
x7 = -pi
$$x_{7} = - \pi$$
-5*pi
x8 = -----
6
$$x_{8} = - \frac{5 \pi}{6}$$
-2*pi
x9 = -----
3
$$x_{9} = - \frac{2 \pi}{3}$$
-pi
x10 = ----
2
$$x_{10} = - \frac{\pi}{2}$$
-pi
x11 = ----
3
$$x_{11} = - \frac{\pi}{3}$$
-pi
x12 = ----
6
$$x_{12} = - \frac{\pi}{6}$$
pi
x13 = --
6
$$x_{13} = \frac{\pi}{6}$$
pi
x14 = --
3
$$x_{14} = \frac{\pi}{3}$$
pi
x15 = --
2
$$x_{15} = \frac{\pi}{2}$$
2*pi
x16 = ----
3
$$x_{16} = \frac{2 \pi}{3}$$
5*pi
x17 = ----
6
$$x_{17} = \frac{5 \pi}{6}$$
x18 = pi
$$x_{18} = \pi$$
7*pi
x19 = ----
6
$$x_{19} = \frac{7 \pi}{6}$$
4*pi
x20 = ----
3
$$x_{20} = \frac{4 \pi}{3}$$
3*pi
x21 = ----
2
$$x_{21} = \frac{3 \pi}{2}$$
5*pi
x22 = ----
3
$$x_{22} = \frac{5 \pi}{3}$$
11*pi
x23 = -----
6
$$x_{23} = \frac{11 \pi}{6}$$
x24 = 2*pi
$$x_{24} = 2 \pi$$
Sum and product of roots
[src]
sum
11*pi 5*pi 3*pi 4*pi 7*pi 5*pi 2*pi pi pi pi pi pi pi 2*pi 5*pi 7*pi 4*pi 3*pi 5*pi 11*pi
0 + 0 - ----- - ---- - ---- - ---- - ---- - pi - ---- - ---- - -- - -- - -- + -- + -- + -- + ---- + ---- + pi + ---- + ---- + ---- + ---- + ----- + 2*pi
6 3 2 3 6 6 3 2 3 6 6 3 2 3 6 6 3 2 3 6
$$\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(- \frac{11 \pi}{6} + \left(0 + 0\right)\right) - \frac{5 \pi}{3}\right) - \frac{3 \pi}{2}\right) - \frac{4 \pi}{3}\right) - \frac{7 \pi}{6}\right) - \pi\right) - \frac{5 \pi}{6}\right) - \frac{2 \pi}{3}\right) - \frac{\pi}{2}\right) - \frac{\pi}{3}\right) - \frac{\pi}{6}\right) + \frac{\pi}{6}\right) + \frac{\pi}{3}\right) + \frac{\pi}{2}\right) + \frac{2 \pi}{3}\right) + \frac{5 \pi}{6}\right) + \pi\right) + \frac{7 \pi}{6}\right) + \frac{4 \pi}{3}\right) + \frac{3 \pi}{2}\right) + \frac{5 \pi}{3}\right) + \frac{11 \pi}{6}\right) + 2 \pi$$
=
2*pi
$$2 \pi$$
product
-11*pi -5*pi -3*pi -4*pi -7*pi -5*pi -2*pi -pi -pi -pi pi pi pi 2*pi 5*pi 7*pi 4*pi 3*pi 5*pi 11*pi
1*0*------*-----*-----*-----*-----*-pi*-----*-----*----*----*----*--*--*--*----*----*pi*----*----*----*----*-----*2*pi
6 3 2 3 6 6 3 2 3 6 6 3 2 3 6 6 3 2 3 6
$$2 \pi \frac{11 \pi}{6} \frac{5 \pi}{3} \frac{3 \pi}{2} \frac{4 \pi}{3} \frac{7 \pi}{6} \pi \frac{5 \pi}{6} \frac{2 \pi}{3} \frac{\pi}{2} \frac{\pi}{3} \frac{\pi}{6} - \frac{\pi}{6} - \frac{\pi}{3} - \frac{\pi}{2} - \frac{2 \pi}{3} - \frac{5 \pi}{6} - \pi - \frac{7 \pi}{6} - \frac{4 \pi}{3} - \frac{3 \pi}{2} - \frac{5 \pi}{3} 1 \cdot 0 \left(- \frac{11 \pi}{6}\right)$$
=
0
$$0$$
0
Numerical answer
[src]
x1 = 32.1140582366957
x2 = 16.2315620435473
x3 = -60.2138591938044
x4 = -1.74532925199433
x5 = 74.0019602845596
x6 = 84.2994028713261
x7 = -69.8131700797732
x8 = 72.2566310325652
x9 = -51.8362787842316
x10 = -8.90117918517108
x11 = -67.71877497738
x12 = -39.7935069454707
x13 = 52.010811709431
x14 = -41.8879020478639
x15 = 58.1194640914112
x16 = -74.0019602845596
x17 = -78.0162175641465
x18 = 26.1799387799149
x19 = -100.007366139275
x20 = 65.6243798749868
x21 = 0.0
x22 = -89.5353906273091
x23 = -75.7472895365539
x24 = -17.8023583703422
x25 = -79.9360797413403
x26 = 10.1229096615671
x27 = 2.0943951023932
x28 = -95.9931088596881
x29 = -57.9449311662117
x30 = 68.0678408277789
x31 = -45.7276264022514
x32 = 76.0963553869528
x33 = -65.9734457253857
x34 = -85.870199198121
x35 = -38.3972435438752
x36 = -19.8967534727354
x37 = 54.1052068118242
x38 = -29.845130209103
x39 = 36.1283155162826
x40 = 64.2281164733913
x41 = -87.9645943005142
x42 = -47.8220215046446
x43 = 80.2851455917392
x44 = 70.162235930172
x45 = -5759.06293280569
x46 = 34.0339204138894
x47 = 8.02851455917392
x48 = 17.4532925199433
x49 = -93.7241808320955
x50 = -21.9911485751286
x51 = 14.1371669411541
x52 = -13.9626340159546
x53 = -31.7649923862968
x54 = 43.9822971502571
x55 = 41.3643032722656
x56 = 56.025068989018
x57 = 42.2369678982628
x58 = -3.83972435438753
x59 = -19.1986217719376
x60 = 24.0855436775217
x61 = 5.23598775598299
x62 = -35.9537825910832
x63 = 46.0766922526503
x64 = 21.9911485751286
x65 = 50.2654824574367
x66 = 92.1533845053006
x67 = -91.8043186549017
x68 = 30.0196631343025
x69 = 82.0304748437335
x70 = -25.8308729295161
x71 = 4.18879020478639
x72 = 77.8416846389471
x73 = -71.733032256967
x74 = -53.7561409614254
x75 = 98.0875039620813
x76 = 100.007366139275
x77 = -82.0304748437335
x78 = 90.0589894029074
x79 = -43.9822971502571
x80 = 63.5299847725936
x81 = -61.7846555205993
x82 = -49.7418836818384
x83 = 95.9931088596881
x84 = 28.2743338823081
x85 = 94.2477796076938
x86 = -56.025068989018
x87 = -5.75958653158129
x88 = 20.2458193231342
x89 = 86.2192650485199
x90 = -23.7364778271229
x91 = -7.85398163397448
x92 = 19.1986217719376
x93 = -63.8790506229925
x94 = -34.0339204138894
x95 = -97.7384381116825
x96 = 38.2227106186758
x97 = -83.7758040957278
x98 = 48.1710873550435
x99 = -27.7507351067098
x99 = -27.7507351067098