Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation cos(x)=1/3
-
Equation x-2(3x+2)=16
-
Equation |x+2|+|x-3|=7
-
Equation 7x^2+8-13x=8x-6
- Express {x} in terms of y where:
- 14*x-16*y=-3
- 17*x-20*y=6
- 10*x-19*y=3
- -2*x-1*y=-8
- Integral of d{x}:
-
sin(2x)
- Derivative of:
-
sin(2x)
- Graphing y =:
- sin(2x)
-
Identical expressions
- sin(2x)= zero . ninety-six
- sinus of (2x) equally 0.96
- sinus of (2x) equally zero . ninety minus six
- sin2x=0.96
- sin(2x)=O.96
-
Similar expressions
- cos^2(x/3)-sin^2(x/3)=1/2
- 2sin^2x+cos^2x-3sinx-5=0
- -4*sin^2(x)-2*sin(x)+2=0
- 2sin^2x+7cosx-5=0
sin(2x)=0.96 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$\sin{\left(2 x \right)} = \frac{24}{25}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$2 x = 2 \pi n + \operatorname{asin}{\left(\frac{24}{25} \right)}$$
$$2 x = 2 \pi n - \operatorname{asin}{\left(\frac{24}{25} \right)} + \pi$$
Or
$$2 x = 2 \pi n + \operatorname{asin}{\left(\frac{24}{25} \right)}$$
$$2 x = 2 \pi n - \operatorname{asin}{\left(\frac{24}{25} \right)} + \pi$$
, where n - is a integer
Divide both parts of the equation by
$$2$$
we get the answer:
$$x_{1} = \pi n + \frac{\operatorname{asin}{\left(\frac{24}{25} \right)}}{2}$$
$$x_{2} = \pi n - \frac{\operatorname{asin}{\left(\frac{24}{25} \right)}}{2} + \frac{\pi}{2}$$
$$\sin{\left(2 x \right)} = \frac{24}{25}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$2 x = 2 \pi n + \operatorname{asin}{\left(\frac{24}{25} \right)}$$
$$2 x = 2 \pi n - \operatorname{asin}{\left(\frac{24}{25} \right)} + \pi$$
Or
$$2 x = 2 \pi n + \operatorname{asin}{\left(\frac{24}{25} \right)}$$
$$2 x = 2 \pi n - \operatorname{asin}{\left(\frac{24}{25} \right)} + \pi$$
, where n - is a integer
Divide both parts of the equation by
$$2$$
we get the answer:
$$x_{1} = \pi n + \frac{\operatorname{asin}{\left(\frac{24}{25} \right)}}{2}$$
$$x_{2} = \pi n - \frac{\operatorname{asin}{\left(\frac{24}{25} \right)}}{2} + \frac{\pi}{2}$$
Rapid solution
[src]
/24\
asin|--|
pi \25/
x1 = -- - --------
2 2
$$x_{1} = - \frac{\operatorname{asin}{\left(\frac{24}{25} \right)}}{2} + \frac{\pi}{2}$$
/24\
asin|--|
\25/
x2 = --------
2
$$x_{2} = \frac{\operatorname{asin}{\left(\frac{24}{25} \right)}}{2}$$
x2 = asin(24/25)/2
Sum and product of roots
[src]
sum
/24\ /24\
asin|--| asin|--|
pi \25/ \25/
-- - -------- + --------
2 2 2
$$\frac{\operatorname{asin}{\left(\frac{24}{25} \right)}}{2} + \left(- \frac{\operatorname{asin}{\left(\frac{24}{25} \right)}}{2} + \frac{\pi}{2}\right)$$
=
pi -- 2
$$\frac{\pi}{2}$$
product
/ /24\\ /24\ | asin|--|| asin|--| |pi \25/| \25/ |-- - --------|*-------- \2 2 / 2
$$\left(- \frac{\operatorname{asin}{\left(\frac{24}{25} \right)}}{2} + \frac{\pi}{2}\right) \frac{\operatorname{asin}{\left(\frac{24}{25} \right)}}{2}$$
=
/ /24\\ /24\
|pi - asin|--||*asin|--|
\ \25// \25/
------------------------
4
$$\frac{\left(\pi - \operatorname{asin}{\left(\frac{24}{25} \right)}\right) \operatorname{asin}{\left(\frac{24}{25} \right)}}{4}$$
(pi - asin(24/25))*asin(24/25)/4
Numerical answer
[src]
x1 = -43.3387960414638
x2 = 51.1927776754383
x3 = -99.8874638060801
x4 = -33.9140180806944
x5 = 72.9001321413585
x6 = -37.0556107342842
x7 = -58.7629652002045
x8 = -49.6219813486434
x9 = 66.6169468341789
x10 = 50.90898356623
x11 = 76.0417247949483
x12 = -14.7806680499474
x13 = -65.3299446165924
x14 = 28.9178349911014
x15 = -55.905166655823
x16 = 35.4848144074893
x17 = 48.0511850218485
x18 = -140.444374193539
x19 = 85.750296864926
x20 = -8.49748274276777
x21 = 29.2016291003098
x22 = 101.458260132875
x23 = 22.6346496839218
x24 = 92.0334821721056
x25 = 13.4936658323608
x26 = 66.9007409433873
x27 = 82.3249101021279
x28 = -93.6042784989005
x29 = -27.3470386643065
x30 = -80.754113775333
x31 = 95.1750748256954
x32 = 16.3514643767422
x33 = 73.1839262505669
x34 = -21.0638533571269
x35 = 6.92668641597287
x36 = -36.7718166250759
x37 = -68.1877431609738
x38 = 41.7679997146689
x39 = -81.0379078845413
x40 = 57.4759629826179
x41 = -52.4797798930249
x42 = 19.7768511395404
x43 = 88.6080954093075
x44 = 60.3337615269994
x45 = -21.3476474663353
x46 = -15.0644621591557
x47 = -5.6396841983863
x48 = -39.9134092786657
x49 = 4.06888787159141
x50 = 10.0682790695627
x51 = 70.0423335969771
x52 = 63.7591482897975
x53 = -71.613129923772
x54 = -77.6125211217432
x55 = 0.643501108793284
x56 = -96.462077043282
x57 = 26.06003644672
x58 = -61.9045578537943
x59 = -24.2054460107167
x60 = -46.1965945858453
x61 = 38.3426129518708
x62 = 54.0505762198198
x63 = -489.444952851214
x64 = -90.1788917361024
x65 = -11.9228695055659
x66 = -59.0467593094128
x67 = -83.8957064289228
x68 = -74.4709284681534
x69 = -2.21429743558818
x70 = -27.6308327735149
x71 = 94.8912807164871
x72 = -87.3210931917209
x73 = 44.6257982590504
x74 = -77.8963152309515
x75 = 19.493057030332
x76 = -33.6302239714861
x77 = 7.2104805251812
x78 = 761.192717386732
x79 = -17.9222607035371
x80 = -30.4886313178963
x81 = 32.0594276446912
x82 = 79.4671115577464
x82 = 79.4671115577464