sin(4*x)=1

Дано

$$\sin{\left (4 x \right )} = 1$$
Подробное решение
Дано уравнение
$$\sin{\left (4 x \right )} = 1$$
— это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$4 x = 2 \pi n + {asin}{\left (1 \right )}$$
$$4 x = 2 \pi n — {asin}{\left (1 \right )} + \pi$$
Или
$$4 x = 2 \pi n + \frac{\pi}{2}$$
$$4 x = 2 \pi n + \frac{\pi}{2}$$
, где n — любое целое число
Разделим обе части полученного ур-ния на
$$4$$
получим ответ:
$$x_{1} = \frac{\pi n}{2} + \frac{\pi}{8}$$
$$x_{2} = \frac{\pi n}{2} + \frac{\pi}{8}$$
Читайте также  (sqrt(5)-1/x)^2+1/(sqrt(5)-1/x) если x=4 (упростите выражение)
Ответ

pi
x1 = —
8

$$x_{1} = \frac{\pi}{8}$$
Численный ответ

x1 = 52.2289777792000

x2 = -56.1559685831000

x3 = -26.3108383511000

x4 = -81.2887099089000

x5 = -21.5984495765000

x6 = 74.2201264654000

x7 = 14.5298659064000

x8 = 83.6449045157000

x9 = -84.4303025070000

x10 = 17.6714587968000

x11 = -29.4524312450000

x12 = 89.9280897692000

x13 = -51.4435798202000

x14 = -35.7356164449000

x15 = 80.5033116353000

x16 = 96.2112750487000

x17 = 72.6493300240000

x18 = 91.4988858631000

x19 = -73.4347283952000

x20 = 3.53429172011000

x21 = -93.8550803968000

x22 = 82.0741078308000

x23 = 31.8086257283000

x24 = -79.7179136069000

x25 = -42.0188021311000

x26 = 1.96349544400000

x27 = -48.3019869255000

x28 = 6.67588432482000

x29 = 66.3661447392000

x30 = 22.3838475811000

x31 = -228.943564807000

x32 = 97.7820714599000

x33 = -12.1736719263000

x34 = 58.5121630588000

x35 = 28.6670328896000

x36 = 52.2289778825000

x37 = -37.3064127982000

x38 = 72.6493300142000

x39 = -62.4391539455000

x40 = -87.5718952244000

x41 = -78.1471171615000

x42 = 39.6626073702000

x43 = 50.6581814561000

x44 = -12.1736714270000

x45 = 30.2378293002000

x46 = -18.4568568312000

x47 = 47.5165888062000

x48 = -100.138265740000

x49 = 94.6404785931000

x50 = -65.5807467335000

x51 = -34.1648200050000

x52 = 75.7909228829000

x53 = 25.5254403437000

x54 = 61.6537559432000

x55 = 69.5077373387000

x56 = 67.9369411885000

x57 = 0.392699002219000

x58 = -43.5895981551000

x59 = 36.5210144825000

x60 = 25.5254402663000

x61 = -86.0010988907000

x62 = -42.0188017217000

x63 = -13.7444678635000

x64 = 23.9546440260000

x65 = -20.0276531385000

x66 = -64.0099503057000

x67 = 45.9457926074000

x68 = -4.31968977693000

x69 = -95.4258769697000

x70 = -7.46128266945000

x71 = -40.4480053867000

x72 = -70.2931355003000

x73 = 44.3749961601000

x74 = -87.5718953118000

x75 = -15.3152642379000

x76 = 9.81747676784000

x77 = 88.3572933185000

x78 = 8.24668071816000

x79 = -59.2975613554000

x80 = 53.7997743057000

x81 = 162.184720622000

x82 = -71.8639318172000

x83 = -57.7267650260000

x84 = -67.1515431778000

x85 = -92.2842840753000

x86 = 9.81747715076000

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