Mister Exam

sinx=0,13 equation

The teacher will be very surprised to see your correct solution 😉

v

Numerical solution:

Do search numerical solution at [, ]

The solution

You have entered [src]
          13
sin(x) = ---
         100
$$\sin{\left(x \right)} = \frac{13}{100}$$
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
The graph
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
sinx=0,13 equation