Mister Exam

Other calculators

sin(5*x)+cos(5*x)=(sqrt(2))*cos(x) equation

The teacher will be very surprised to see your correct solution 😉

v

Numerical solution:

Do search numerical solution at [, ]

The solution

You have entered [src]
                        ___       
sin(5*x) + cos(5*x) = \/ 2 *cos(x)
$$\sin{\left(5 x \right)} + \cos{\left(5 x \right)} = \sqrt{2} \cos{\left(x \right)}$$
The graph
Sum and product of roots [src]
sum
0
$$0$$
=
0
$$0$$
product
1
$$1$$
=
1
$$1$$
1
Numerical answer [src]
x1 = 46.2075919465499
x2 = -19.7658537788358
x3 = 48.3019870489431
x4 = -85.7392995042214
x5 = -81.550509299435
x6 = 26.3108384738145
x7 = -100.400065220974
x8 = -89.9280897090078
x9 = -6.08683576633022
x10 = -23.9546439836222
x11 = 74.0237769002095
x12 = 17.4751091355932
x13 = -99.3528676697772
x14 = 94.3786793015934
x15 = -28.0779843414588
x16 = 101.70906215997
x17 = 6.41408500107916
x18 = 28.4052335762077
x19 = 59.8866099590554
x20 = -41.7570023539643
x21 = 30.0414797499524
x22 = -52.2289778659303
x23 = 66.169795266235
x24 = -17.6714586764426
x25 = -79.9142631256904
x26 = -87.7682447596649
x27 = -63.7481509290929
x28 = -94.0514300668444
x29 = 96.0149254753381
x30 = 44.1786466911065
x31 = -15.5770635740494
x32 = 64.009950316892
x33 = -57.4649656219133
x34 = 50.3963821513363
x35 = 61.9155552144988
x36 = -70.0313362362725
x37 = 68.1987405216784
x38 = 52.4907772537295
x39 = -61.6537558266997
x40 = 2.22529479629277
x41 = 14.3335164820034
x42 = -37.5682121491779
x43 = 22.1874981159779
x44 = 80.3069622073891
x45 = 42.0188017417635
x46 = -59.5593607243065
x47 = -65.7770961845363
x48 = -7.65763209312512
x49 = -34.3611696486384
x50 = -73.6310778185108
x51 = 8.05033117482385
x52 = 86.0010988920206
x53 = 52.0326283250809
x54 = -72.0602814917159
x55 = 15.9043128087983
x56 = 58.3158136322605
x57 = -39.6626072515711
x58 = -43.7859476094077
x59 = 79.717913584841
x60 = -78.4089166458453
x61 = 83.9067037896274
x62 = -35.9319659754333
x63 = -21.7947990342792
x64 = -57.9231145505618
x65 = 90.189889096807
x66 = 20.0276531666349
x67 = -45.9457925587507
x68 = -13.9408174003047
x69 = 56.7450173054656
x70 = -67.9369411338793
x71 = -92.022484811401
x72 = -75.2673239922555
x73 = -29.6487806682537
x74 = 70.2931356240716
x75 = 4.31968989868597
x76 = 24.2164433714213
x77 = 73.4347282776614
x78 = -83.6449044018282
x79 = 37.8954613839269
x80 = -50.0691329165873
x81 = -1.96349540849362
x82 = -48.0401876611439
x83 = 72.3875307264648
x84 = 36.324665057132
x85 = 81.877758534184
x86 = 39.9244066393703
x87 = -51.6399292433822
x88 = 92.2842841992002
x89 = 59.8211601121056
x90 = 17.9332580642417
x91 = -95.6222263936393
x92 = -26.0490390860154
x93 = 10.6028752058656
x94 = -4.05789051088682
x95 = 0.196349540849362
x95 = 0.196349540849362