Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation 2(x+4)(x+2)=x^2+2x
-
Equation sin4x=1
-
Equation sqrt(2*cos(x))-1=0
- Equation sin(x)=1/sqrt(2)
- Express {x} in terms of y where:
- (x^2+y^2-1)^3+x^2*y^3=0
- 4*x-16*y=6
- -1*x-19*y=-10
- 5*x+5*y=20
- Derivative of:
-
sin4x
- Graphing y =:
- sin4x
- Integral of d{x}:
-
sin4x
-
Identical expressions
- sin4x= one
- sinus of 4x equally 1
- sinus of 4x equally one
-
Similar expressions
- cos(8*x)+7*sin(4*x)-6=0
- 2cos^2(2x)-2sin(4x)+1=0
sin4x=1 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$\sin{\left(4 x \right)} = 1$$
- this is the simplest trigonometric equation
This equation is transformed to
$$4 x = 2 \pi n + \operatorname{asin}{\left(1 \right)}$$
$$4 x = 2 \pi n - \operatorname{asin}{\left(1 \right)} + \pi$$
Or
$$4 x = 2 \pi n + \frac{\pi}{2}$$
$$4 x = 2 \pi n + \frac{\pi}{2}$$
, where n - is a integer
Divide both parts of the equation by
$$4$$
we get the answer:
$$x_{1} = \frac{\pi n}{2} + \frac{\pi}{8}$$
$$x_{2} = \frac{\pi n}{2} + \frac{\pi}{8}$$
$$\sin{\left(4 x \right)} = 1$$
- this is the simplest trigonometric equation
This equation is transformed to
$$4 x = 2 \pi n + \operatorname{asin}{\left(1 \right)}$$
$$4 x = 2 \pi n - \operatorname{asin}{\left(1 \right)} + \pi$$
Or
$$4 x = 2 \pi n + \frac{\pi}{2}$$
$$4 x = 2 \pi n + \frac{\pi}{2}$$
, where n - is a integer
Divide both parts of the equation by
$$4$$
we get the answer:
$$x_{1} = \frac{\pi n}{2} + \frac{\pi}{8}$$
$$x_{2} = \frac{\pi n}{2} + \frac{\pi}{8}$$
Sum and product of roots
[src]
sum
pi -- 8
$$\left(\frac{\pi}{8}\right)$$
=
pi -- 8
$$\frac{\pi}{8}$$
product
pi -- 8
$$\left(\frac{\pi}{8}\right)$$
=
pi -- 8
$$\frac{\pi}{8}$$
Numerical answer
[src]
x1 = -37.3064127981981
x2 = 91.4988858631041
x3 = 47.5165888062105
x4 = 52.2289778825359
x5 = -84.430302507019
x6 = -26.3108383510529
x7 = -13.7444678635051
x8 = 58.5121630587909
x9 = -71.8639318172356
x10 = -42.018801721698
x11 = 83.6449045156666
x12 = 44.3749961600903
x13 = -35.7356164448818
x14 = 6.67588432482476
x15 = 17.6714587968444
x16 = 80.5033116353485
x17 = 36.5210144824622
x18 = 9.81747715075509
x19 = 31.808625728328
x20 = -73.4347283951574
x21 = 74.2201264653626
x22 = -87.5718953117726
x23 = -12.1736719262543
x24 = -40.4480053866604
x25 = 9.81747676783862
x26 = 82.0741078307881
x27 = 52.2289777791699
x28 = -48.3019869255039
x29 = 67.9369411885029
x30 = 8.24668071816113
x31 = 25.525440266285
x32 = 61.6537559431866
x33 = 53.7997743057058
x34 = -18.4568568311997
x35 = 23.9546440259598
x36 = 88.3572933185348
x37 = -81.2887099089205
x38 = -64.009950305697
x39 = -12.1736714270123
x40 = -70.2931355002572
x41 = 30.2378293001575
x42 = -20.0276531385131
x43 = 50.6581814561062
x44 = 0.392699002218603
x45 = -79.7179136068893
x46 = 69.5077373387294
x47 = 3.53429172010594
x48 = -95.4258769697172
x49 = 94.6404785931085
x50 = 75.7909228828866
x51 = -67.1515431778245
x52 = -42.0188021311225
x53 = 39.6626073702294
x54 = 22.3838475810827
x55 = 28.6670328896188
x56 = -4.31968977692752
x57 = 45.9457926074387
x58 = -43.5895981550743
x59 = -29.4524312449951
x60 = -59.2975613554301
x61 = 25.5254403437163
x62 = -92.2842840752935
x63 = -93.8550803968028
x64 = -87.5718952244412
x65 = -62.4391539454797
x66 = 72.6493300240099
x67 = -34.1648200049742
x68 = -228.943564806969
x69 = -15.3152642379275
x70 = 89.9280897692015
x71 = 97.782071459868
x72 = 96.2112750487236
x73 = -56.1559685831317
x74 = -65.5807467334992
x75 = 162.184720622203
x76 = 14.5298659063767
x77 = -78.1471171614871
x78 = -57.7267650260013
x79 = 66.3661447392409
x80 = -7.46128266944874
x81 = -51.4435798202399
x82 = 1.96349544400331
x83 = -21.598449576501
x84 = 72.6493300141926
x85 = -86.00109889071
x86 = -100.138265740044
x86 = -100.138265740044
The graph