Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation (x-5)/2=2*(3x/7-1/2)/3
-
Equation (x^2-4)^2+(x^2-3*x-10)^2=0
-
Equation x^2=-16
-
Equation sin(x)=-1
- Express {x} in terms of y where:
- 16*x-17*y=-9
- -7*x-7*y=-14
- -15*x+17*y=13
- 4*x-15*y=19
- Sum of series:
- sinx
-
7/10
- Graphing y =:
- sinx
- Integral of d{x}:
-
sinx
-
Identical expressions
- sinx= seven / ten
- sinus of x equally 7 divide by 10
- sinus of x equally seven divide by ten
- sinx=7 divide by 10
-
Similar expressions
- sin(x)=-1/5
- sin(x)=-1
sinx=7/10 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$\sin{\left(x \right)} = \frac{7}{10}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$x = 2 \pi n + \operatorname{asin}{\left(\frac{7}{10} \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(\frac{7}{10} \right)} + \pi$$
Or
$$x = 2 \pi n + \operatorname{asin}{\left(\frac{7}{10} \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(\frac{7}{10} \right)} + \pi$$
, where n - is a integer
$$\sin{\left(x \right)} = \frac{7}{10}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$x = 2 \pi n + \operatorname{asin}{\left(\frac{7}{10} \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(\frac{7}{10} \right)} + \pi$$
Or
$$x = 2 \pi n + \operatorname{asin}{\left(\frac{7}{10} \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(\frac{7}{10} \right)} + \pi$$
, where n - is a integer
Rapid solution
[src]
x1 = pi - asin(7/10)
$$x_{1} = \pi - \operatorname{asin}{\left(\frac{7}{10} \right)}$$
x2 = asin(7/10)
$$x_{2} = \operatorname{asin}{\left(\frac{7}{10} \right)}$$
x2 = asin(7/10)
Sum and product of roots
[src]
sum
pi - asin(7/10) + asin(7/10)
$$\operatorname{asin}{\left(\frac{7}{10} \right)} + \left(\pi - \operatorname{asin}{\left(\frac{7}{10} \right)}\right)$$
=
pi
$$\pi$$
product
(pi - asin(7/10))*asin(7/10)
$$\left(\pi - \operatorname{asin}{\left(\frac{7}{10} \right)}\right) \operatorname{asin}{\left(\frac{7}{10} \right)}$$
=
(pi - asin(7/10))*asin(7/10)
$$\left(\pi - \operatorname{asin}{\left(\frac{7}{10} \right)}\right) \operatorname{asin}{\left(\frac{7}{10} \right)}$$
(pi - asin(7/10))*asin(7/10)
Numerical answer
[src]
x1 = 38.4745093396883
x2 = -91.8815844507148
x3 = 76.1736211827658
x4 = -99.7555674182626
x5 = -43.2068996536464
x6 = -66.7488432219964
x7 = 32.1913240325087
x8 = -74.6228261895443
x9 = -1614.00322644854
x10 = -35.3329166860985
x11 = 40.0653070000566
x12 = -5.50778781056883
x13 = -79.3152138363556
x14 = -135.863881600972
x15 = 71.4812335359545
x16 = -47.8992873004577
x17 = -343.208996737898
x18 = -36.9237143464668
x19 = -93.472382111083
x20 = 0.775397496610753
x21 = 8.64938046415863
x22 = -68.3396408823647
x23 = 65.1980482287749
x24 = 69.8904358755862
x25 = -236.394846515845
x26 = -29.0497313789189
x27 = -3.91699015020055
x28 = -62.0564555751851
x29 = -60.4656579148168
x30 = -87.1891968039035
x31 = 51.0408799540474
x32 = 3645.02287566077
x33 = -85.5983991435352
x34 = -18.074158424928
x35 = 90.3307894574933
x36 = 21.2157510785178
x37 = -49.4900849608259
x38 = 84.0476041503137
x39 = 77.7644188431341
x40 = 101.306362411484
x41 = -30.6405290392872
x42 = 7.05858280379034
x43 = -98.1647697578943
x44 = -55.7732702680055
x45 = -10.2001754573801
x46 = -16.4833607645597
x47 = 2.36619515697904
x48 = 13.3417681109699
x49 = -2550.1978372183
x50 = 25.9081387253291
x51 = 44.7576946468679
x52 = -11.7909731177484
x53 = 96.6139747646728
x54 = 2704.1358772442
x55 = 8522.3654716925
x56 = -80.9060114967239
x57 = 63.6072505684066
x58 = 82.4568064899454
x59 = 88.739991797125
x60 = -24.3573437321076
x61 = 58.9148629215953
x62 = 14.9325657713382
x63 = 33.782121692877
x64 = 19.6249534181495
x65 = -41.6161019932781
x66 = 46.3484923072361
x67 = -54.1824726076372
x68 = 95.0231771043046
x69 = 27.4989363856974
x70 = 52.6316776144157
x71 = 113.872733025843
x72 = -22.7665460717393
x73 = 57.324065261227
x74 = -73.032028529176
x74 = -73.032028529176