Mister Exam
Other calculators
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How to use it?
- Equation:
- Equation 2x^2-50=0
-
Equation sinx=0,13
- Equation x^2-14/x-10x/x^2-14=3
-
Equation x^4-2x^2+1=0
- Express {x} in terms of y where:
- 15*x-15*y=16
- 9*x+18*y=6
- (x^2+y^2-1)^3+x^2*y^3=0
- -1*x-19*y=-10
- Sum of series:
- sinx
-
0,13
- Graphing y =:
- sinx
- Integral of d{x}:
-
sinx
-
Identical expressions
- sinx= zero , thirteen
- sinus of x equally 0,13
- sinus of x equally zero , thirteen
- sinx=O,13
-
Similar expressions
- (29,97+((0,1*30*x+2*0,03-30)*e^(0,1*x))-(0,03*e^(0,1*2*x)))=0
- sin(x)*sin(7x)=1
- 1440=(13600x+(0,1^3-x)700)10
- (30-0,03)+(0,1*30*x+2*0,03-30)*2,7^(0,1*x)-0,03*2,7^(2*0,1*x)=0
sinx=0,13 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$\sin{\left(x \right)} = \frac{13}{100}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$x = 2 \pi n + \operatorname{asin}{\left(\frac{13}{100} \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(\frac{13}{100} \right)} + \pi$$
Or
$$x = 2 \pi n + \operatorname{asin}{\left(\frac{13}{100} \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(\frac{13}{100} \right)} + \pi$$
, where n - is a integer
$$\sin{\left(x \right)} = \frac{13}{100}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$x = 2 \pi n + \operatorname{asin}{\left(\frac{13}{100} \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(\frac{13}{100} \right)} + \pi$$
Or
$$x = 2 \pi n + \operatorname{asin}{\left(\frac{13}{100} \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(\frac{13}{100} \right)} + \pi$$
, where n - is a integer
Rapid solution
[src]
/ 13\
x_1 = pi - asin|---|
\100/
$$x_{1} = - \operatorname{asin}{\left(\frac{13}{100} \right)} + \pi$$
/ 13\
x_2 = asin|---|
\100/
$$x_{2} = \operatorname{asin}{\left(\frac{13}{100} \right)}$$
Sum and product of roots
[src]
sum
/ 13\ / 13\
pi - asin|---| + asin|---|
\100/ \100/
$$\left(- \operatorname{asin}{\left(\frac{13}{100} \right)} + \pi\right) + \left(\operatorname{asin}{\left(\frac{13}{100} \right)}\right)$$
=
pi
$$\pi$$
product
/ 13\ / 13\
pi - asin|---| * asin|---|
\100/ \100/
$$\left(- \operatorname{asin}{\left(\frac{13}{100} \right)} + \pi\right) * \left(\operatorname{asin}{\left(\frac{13}{100} \right)}\right)$$
=
/ / 13\\ / 13\ |pi - asin|---||*asin|---| \ \100// \100/
$$\left(- \operatorname{asin}{\left(\frac{13}{100} \right)} + \pi\right) \operatorname{asin}{\left(\frac{13}{100} \right)}$$
Numerical answer
[src]
x1 = 15.5775942882458
x2 = 31.5462955156011
x3 = -84.9533706266276
x4 = -18.7191869418356
x5 = 56.6790367443194
x6 = -50.1351134777335
x7 = -78.670185319448
x8 = 18.9799249012419
x9 = 40.7103355169642
x10 = -3.27196163329294
x11 = 9.29440898106623
x12 = -81.5510400136315
x13 = -94.1174106279907
x14 = -31.2855575561948
x15 = 53.2767061313233
x16 = -47.25425878355
x17 = -40.9710734763705
x18 = 28.143964902605
x19 = 62.962222051499
x20 = 34.4271502097846
x21 = -37.5687428633744
x22 = -68.9846693992723
x23 = -56.4182987849131
x24 = 65.8430767456825
x25 = -87.8342253208111
x26 = -43.851928170554
x27 = 37.8294808227807
x28 = -66.1038147050888
x29 = -75.2678547064519
x30 = -2619.95790411418
x31 = -34.6878881691909
x32 = -97.5197412409867
x33 = 3.01122367388665
x34 = 12.6967395940623
x35 = -25.0023722490152
x36 = -6.15281632747644
x37 = 84.6926326672213
x38 = -9.55514694047253
x39 = 46.9935208241438
x40 = -62.7014840920927
x41 = -72.3870000122684
x42 = 90.9758179744009
x43 = 25.2631102084215
x44 = -28.4047028620113
x45 = 50.3958514371398
x46 = 78.4094473600417
x47 = 97.2590032815804
x48 = -53.5374440907296
x49 = 72.1262620528621
x50 = 88.0949632802174
x51 = -329.997597606631
x52 = 618.763383777486
x53 = 6.41355428688273
x54 = 69.2454073586786
x55 = 81.8117779730378
x56 = -91.2365559338072
x57 = -100.40059593517
x58 = 0.130368979703146
x59 = 94.3781485873969
x60 = 21.8607795954254
x61 = 75.5285926658582
x62 = -116.369297162525
x63 = 44.1126661299603
x64 = -59.8206293979092
x65 = -12.436001634656
x66 = 59.5598914385029
x67 = 100.661333894577
x68 = -22.1215175548317
x69 = -15.8383322476521
x69 = -15.8383322476521
The graph