Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation 25*x^3-10*x^2+x=0
-
Equation 2x^2-x-1=x^2-5x-(-1-x^2)
-
Equation 2^x=5
-
Equation (x-10)^2=(x+4)^2
- Express {x} in terms of y where:
- 15*x+12*y=-19
- -19*x-20*y=-4
- -18*x+12*y=-8
- -14*x+4*y=-16
-
Identical expressions
- -(sin(x)+cos(x)/ two)= zero
- minus ( sinus of (x) plus co sinus of e of (x) divide by 2) equally 0
- minus ( sinus of (x) plus co sinus of e of (x) divide by two) equally zero
- -sinx+cosx/2=0
- -(sin(x)+cos(x)/2)=O
- -(sin(x)+cos(x) divide by 2)=0
-
Similar expressions
- -(sin(x)-cos(x)/2)=0
- (sin(x)+cos(x)/2)=0
- -(sinx+cosx/2)=0
-(sin(x)+cos(x)/2)=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
cos(x)
-sin(x) - ------ = 0
2
$$- \sin{\left(x \right)} - \frac{\cos{\left(x \right)}}{2} = 0$$
Detail solution
Given the equation
$$- \sin{\left(x \right)} - \frac{\cos{\left(x \right)}}{2} = 0$$
transform:
$$- \frac{\sin{\left(x \right)}}{\cos{\left(x \right)}} = \frac{1}{2}$$
or
$$- \tan{\left(x \right)} = \frac{1}{2}$$
- this is the simplest trigonometric equation
The equation is transformed to
$$\tan{\left(x \right)} = \frac{1}{2}$$
This equation is transformed to
$$x = \pi n + \operatorname{atan}{\left(\frac{1}{2} \right)}$$
Or
$$x = \pi n + \operatorname{atan}{\left(\frac{1}{2} \right)}$$
, where n - is a integer
$$- \sin{\left(x \right)} - \frac{\cos{\left(x \right)}}{2} = 0$$
transform:
$$- \frac{\sin{\left(x \right)}}{\cos{\left(x \right)}} = \frac{1}{2}$$
or
$$- \tan{\left(x \right)} = \frac{1}{2}$$
- this is the simplest trigonometric equation
Divide both parts of the equation by -1
The equation is transformed to
$$\tan{\left(x \right)} = \frac{1}{2}$$
This equation is transformed to
$$x = \pi n + \operatorname{atan}{\left(\frac{1}{2} \right)}$$
Or
$$x = \pi n + \operatorname{atan}{\left(\frac{1}{2} \right)}$$
, where n - is a integer
Rapid solution
[src]
x1 = -atan(1/2)
$$x_{1} = - \operatorname{atan}{\left(\frac{1}{2} \right)}$$
x1 = -atan(1/2)
Sum and product of roots
[src]
sum
-atan(1/2)
$$- \operatorname{atan}{\left(\frac{1}{2} \right)}$$
=
-atan(1/2)
$$- \operatorname{atan}{\left(\frac{1}{2} \right)}$$
product
-atan(1/2)
$$- \operatorname{atan}{\left(\frac{1}{2} \right)}$$
=
-atan(1/2)
$$- \operatorname{atan}{\left(\frac{1}{2} \right)}$$
-atan(1/2)
Numerical answer
[src]
x1 = -16.1716108769498
x2 = -35.0211667984885
x3 = 15.2443156589482
x4 = 34.0938715804869
x5 = -53.8707227200273
x6 = 62.3682054627951
x7 = -9.88842556977019
x8 = -97.8530198702844
x9 = 2.67794504458899
x10 = 43.5186495412563
x11 = -57.0123153736171
x12 = -72.7202786415661
x13 = 37.2354642340767
x14 = -91.5698345631048
x15 = -50.7291300664375
x16 = -286.348579085672
x17 = -63.2955006807967
x18 = 40.3770568876665
x19 = -94.7114272166946
x20 = 56.0850201556155
x21 = 71.7929834235644
x22 = 68.6513907699746
x23 = 835.199998245884
x24 = -31.8795741448987
x25 = 78.076168730744
x26 = -82.1450566023354
x27 = -38.1627594520783
x28 = 90.6425393451032
x29 = 24.6690936197175
x30 = -88.428241909515
x31 = 96.9257246522828
x32 = -60.1539080272069
x33 = -19.3132035305396
x34 = 49.8018348484359
x35 = -41.3043521056681
x36 = 21.5275009661277
x37 = 46.6602421948461
x38 = 18.385908312538
x39 = 52.9434275020257
x40 = -44.4459447592579
x41 = -22.4547961841294
x42 = 5.81953769817878
x43 = 27.8106862733073
x44 = 30.9522789268971
x45 = -141.835317020542
x46 = -85.2866492559252
x47 = -100.994612523874
x48 = -28.7379814913089
x49 = 100.067317305873
x50 = -25.5963888377192
x51 = -3.6052402625906
x52 = -0.463647609000806
x53 = -47.5875374128477
x54 = -79.0034639487456
x55 = 8.96113035176857
x56 = 84.3593540379236
x57 = 59.2266128092053
x58 = 191.173504259977
x59 = 81.2177613843338
x60 = -6.74683291618039
x61 = 12.1027230053584
x62 = 87.5009466915134
x63 = 93.784131998693
x64 = -66.4370933343865
x65 = -13.03001822336
x66 = -75.8618712951559
x67 = 65.5097981163849
x68 = 74.9345760771542
x69 = -69.5786859879763
x69 = -69.5786859879763