Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation x^2+5x+6=0
-
Equation 6x+1=-4x
- Equation (3x−36)⋅(x+8)=0
-
Equation 3*x^2+2*x-1=0
- Express {x} in terms of y where:
- 5*x-13*y=17
- 13*x-12*y=19
- -11*x-3*y=14
- -13*x+7*y=-15
-
Identical expressions
- cos(x)*sin(x)+sqrt(two)/ two *cos(x)-sqrt(two)/ two *sin(x)-(one / two)= zero
- co sinus of e of (x) multiply by sinus of (x) plus square root of (2) divide by 2 multiply by co sinus of e of (x) minus square root of (2) divide by 2 multiply by sinus of (x) minus (1 divide by 2) equally 0
- co sinus of e of (x) multiply by sinus of (x) plus square root of (two) divide by two multiply by co sinus of e of (x) minus square root of (two) divide by two multiply by sinus of (x) minus (one divide by two) equally zero
- cos(x)*sin(x)+√(2)/2*cos(x)-√(2)/2*sin(x)-(1/2)=0
- cos(x)sin(x)+sqrt(2)/2cos(x)-sqrt(2)/2sin(x)-(1/2)=0
- cosxsinx+sqrt2/2cosx-sqrt2/2sinx-1/2=0
- cos(x)*sin(x)+sqrt(2)/2*cos(x)-sqrt(2)/2*sin(x)-(1/2)=O
- cos(x)*sin(x)+sqrt(2) divide by 2*cos(x)-sqrt(2) divide by 2*sin(x)-(1 divide by 2)=0
-
Similar expressions
- cos(x)*sin(x)-sqrt(2)/2*cos(x)-sqrt(2)/2*sin(x)-(1/2)=0
- cos(x)*sin(x)+sqrt(2)/2*cos(x)+sqrt(2)/2*sin(x)-(1/2)=0
- cos(x)*sin(x)+sqrt(2)/2*cos(x)-sqrt(2)/2*sin(x)+(1/2)=0
- cosx*sinx+sqrt(2)/2*cosx-sqrt(2)/2*sinx-(1/2)=0
cos(x)*sin(x)+sqrt(2)/2*cos(x)-sqrt(2)/2*sin(x)-(1/2)=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
___ ___
\/ 2 \/ 2 1
cos(x)*sin(x) + -----*cos(x) - -----*sin(x) - - = 0
2 2 2
$$\left(\left(\sin{\left(x \right)} \cos{\left(x \right)} + \frac{\sqrt{2}}{2} \cos{\left(x \right)}\right) - \frac{\sqrt{2}}{2} \sin{\left(x \right)}\right) - \frac{1}{2} = 0$$
Sum and product of roots
[src]
sum
3*pi pi pi - ---- - -- + -- 4 4 4
$$\left(- \frac{3 \pi}{4} - \frac{\pi}{4}\right) + \frac{\pi}{4}$$
=
-3*pi ----- 4
$$- \frac{3 \pi}{4}$$
product
-3*pi -pi pi -----*----*-- 4 4 4
$$\frac{\pi}{4} \cdot - \frac{3 \pi}{4} \left(- \frac{\pi}{4}\right)$$
=
3 3*pi ----- 64
$$\frac{3 \pi^{3}}{64}$$
3*pi^3/64
Rapid solution
[src]
-3*pi
x1 = -----
4
$$x_{1} = - \frac{3 \pi}{4}$$
-pi
x2 = ----
4
$$x_{2} = - \frac{\pi}{4}$$
pi
x3 = --
4
$$x_{3} = \frac{\pi}{4}$$
x3 = pi/4
Numerical answer
[src]
x1 = 51.0508806208341
x2 = -74.6128255227576
x3 = -33.7721210260903
x4 = 3.92699081698724
x5 = 16.4933614313464
x6 = 87.179194571984
x7 = 29.0597320457056
x8 = 60.4756585816035
x9 = -99.7455667514759
x10 = 74.6128253583021
x11 = 80.896010725149
x12 = -88.7499919932625
x13 = 11.7809725867768
x14 = -55.7632696012188
x15 = -7.06858351214916
x16 = -14.9225651045515
x17 = 63.6172512351933
x18 = 32.2013246992954
x19 = 55.763269743648
x20 = -63.6172513138819
x21 = 57.3340659280137
x22 = -90.3207887907066
x23 = -25.918140046808
x24 = 87.1791957824773
x25 = 24.3473430048829
x26 = 79.3252145031423
x27 = 5.49778732761904
x28 = -19.6349541546828
x29 = 91.8915851175014
x30 = 73.0420291959627
x31 = 68.3296401648505
x32 = -95.0331776963524
x33 = -71.4712328691678
x34 = -36.9137136796801
x35 = -76.1836207058187
x36 = 36.9137136019555
x37 = 13.3517687777566
x38 = -7.06858278595795
x39 = -88.7499927410741
x40 = -51.050879648505
x41 = 47.9092879672443
x42 = -11.7809724509617
x43 = -62.0464549083984
x44 = -18.0641577581413
x45 = 43.196900220913
x46 = 82.4668071567321
x47 = 54.1924732744239
x48 = -49.4800842940392
x49 = -38.484509820882
x50 = 7.06858347057703
x51 = 62.0464548193084
x52 = -0.785398387140928
x53 = -77.7544181763474
x54 = -46.3384916404494
x55 = -7.06858433593904
x56 = 18.0641575840826
x57 = 22.776546738526
x58 = -95.0331780630375
x59 = 19.6349540849362
x60 = 30.6305273736884
x61 = 93.4623816213382
x62 = -80.8960108299372
x63 = 30.6305282041351
x64 = -76.1836217282209
x65 = 76.1836218495525
x66 = 69.9004365423729
x67 = 55.7632696992475
x68 = -51.0508806134381
x69 = 98.174770424681
x70 = 531.714556620072
x71 = 43.196898824959
x72 = -44.7676957361531
x73 = -24.3473430653209
x74 = -93.4623814442964
x75 = -27.4889357189107
x76 = -13.3517689495277
x77 = -30.6305283725005
x78 = -57.3340661026433
x79 = -0.785398070020699
x80 = -84.037603483527
x81 = 10.2101761241668
x82 = -32.2013245705094
x83 = 36.9137133992238
x84 = 25.9181393921158
x85 = 49.480084433185
x86 = -68.329640215578
x87 = -65.1880475619882
x88 = -40.0553063332699
x89 = -44.7676949864154
x90 = -58.9048622548086
x91 = 49.4800844750815
x92 = -82.4668069702928
x93 = 38.484510006475
x94 = 95.0331777710912
x95 = -5.49778714378214
x96 = 99.745566900108
x97 = -21.2057504117311
x98 = 66.7588438887831
x98 = 66.7588438887831