Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation e^x=0
-
Equation x^2+2x-3=0
-
Equation -x-7=x
-
Equation tan(x)=-2
- Express {x} in terms of y where:
- 2*x+2*y=-6
- 12*x-13*y=-14
- 4*x-1*y=-3
- 1*x+5*y=-11
- Integral of d{x}:
-
sint
-
-1/2
- Derivative of:
-
sint
- -1/2
- Limit of the function:
- -1/2
-
Identical expressions
- sint=- one / two
- sinus of t equally minus 1 divide by 2
- sinus of t equally minus one divide by two
- sint=-1 divide by 2
-
Similar expressions
- cos(x/2)=-(1/2)
- sint=+1/2
- log(y-1)/2-log(y+1)/2=Const-x
- sin(x-(1/2))-x+(1/2)=0
- sin(t)=-(1/2)*sqrt(2)
- y=c^1*e^t*sin(t)
- -4*(2*cos(t)-(3/2))*sin(t)+2*sin(t*cos(t))=0
sint=-1/2 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$\sin{\left(t \right)} = - \frac{1}{2}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$t = 2 \pi n + \operatorname{asin}{\left(- \frac{1}{2} \right)}$$
$$t = 2 \pi n - \operatorname{asin}{\left(- \frac{1}{2} \right)} + \pi$$
Or
$$t = 2 \pi n - \frac{\pi}{6}$$
$$t = 2 \pi n + \frac{7 \pi}{6}$$
, where n - is a integer
$$\sin{\left(t \right)} = - \frac{1}{2}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$t = 2 \pi n + \operatorname{asin}{\left(- \frac{1}{2} \right)}$$
$$t = 2 \pi n - \operatorname{asin}{\left(- \frac{1}{2} \right)} + \pi$$
Or
$$t = 2 \pi n - \frac{\pi}{6}$$
$$t = 2 \pi n + \frac{7 \pi}{6}$$
, where n - is a integer
Sum and product of roots
[src]
sum
pi 7*pi - -- + ---- 6 6
$$- \frac{\pi}{6} + \frac{7 \pi}{6}$$
=
pi
$$\pi$$
product
-pi 7*pi ----*---- 6 6
$$- \frac{\pi}{6} \frac{7 \pi}{6}$$
=
2 -7*pi ------ 36
$$- \frac{7 \pi^{2}}{36}$$
-7*pi^2/36
Rapid solution
[src]
-pi
t1 = ----
6
$$t_{1} = - \frac{\pi}{6}$$
7*pi
t2 = ----
6
$$t_{2} = \frac{7 \pi}{6}$$
t2 = 7*pi/6
Numerical answer
[src]
t1 = -15.1843644923507
t2 = -8.90117918517108
t3 = -38.2227106186758
t4 = -195.302343298165
t5 = 74.8746249105567
t6 = 437.20497762458
t7 = -84.2994028713261
t8 = -69.6386371545737
t9 = 49.7418836818384
t10 = 93.7241808320955
t11 = -34.0339204138894
t12 = -25.6563400043166
t13 = -82.2050077689329
t14 = -96.8657734856853
t15 = -40.317105721069
t16 = 37.1755130674792
t17 = 81.1578102177363
t18 = -57.0722665402146
t19 = 9.94837673636768
t20 = -63.3554518473942
t21 = 22.5147473507269
t22 = 91.6297857297023
t23 = 41.3643032722656
t24 = 5.75958653158129
t25 = -31.9395253114962
t26 = -101.054563690472
t27 = 30.8923277602996
t28 = 56.025068989018
t29 = 97.9129710368819
t30 = -151.320046147908
t31 = 100.007366139275
t32 = -94.7713783832921
t33 = -59.1666616426078
t34 = 12.0427718387609
t35 = -21.4675497995303
t36 = -6.80678408277789
t37 = 66.497044500984
t38 = 192.160750644576
t39 = 85.3466004225227
t40 = -78.0162175641465
t41 = -46.6002910282486
t42 = 79.0634151153431
t43 = -50.789081233035
t44 = -44.5058959258554
t45 = -27.7507351067098
t46 = -71.733032256967
t47 = 68.5914396033772
t48 = 66400.1787274983
t49 = 62.3082542961976
t50 = 53.9306738866248
t51 = 24.60914245312
t52 = 3.66519142918809
t53 = 72.7802298081635
t54 = -2.61799387799149
t55 = -75.9218224617533
t56 = 87.4409955249159
t57 = -88.4881930761125
t58 = 43.4586983746588
t59 = 28.7979326579064
t60 = 60.2138591938044
t61 = -52.8834763354282
t62 = 47.6474885794452
t63 = 16.2315620435473
t64 = -13.0899693899575
t65 = 35.081117965086
t66 = 18.3259571459405
t67 = -90.5825881785057
t68 = -19.3731546971371
t69 = -0.523598775598299
t70 = -65.4498469497874
t70 = -65.4498469497874