Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation ctg(x)=-5
-
Equation Sqrt(cos^2x-sin^2x)(tg2x-1)=0
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Equation sint=0.5
- Equation (2sin((3pi)/2+2x)^2+sin(4x))/log3(2^(1/2)*sinx)=0
- Express {x} in terms of y where:
- 4*x-16*y=6
- sqrt(x^2+y^2+4x-6y-12)+(x^2+10x-27)=8-|y-9|+|y-3|
- 10*x-1*y=10
- 15*x-17*y=19
- Integral of d{x}:
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sint
- 0.5
- Derivative of:
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sint
- Sum of series:
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0.5
- 0.5
-
Identical expressions
- sint= zero . five
- sinus of t equally 0.5
- sinus of t equally zero . five
- sint=O.5
-
Similar expressions
- sin(t)=1/3
sint=0.5 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
$$t = 2 \pi n + \frac{\pi}{6}$$
$$t = 2 \pi n + \frac{5 \pi}{6}$$
, 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
$$t = 2 \pi n + \frac{\pi}{6}$$
$$t = 2 \pi n + \frac{5 \pi}{6}$$
, where n - is a integer
Rapid solution
[src]
pi
t_1 = --
6
$$t_{1} = \frac{\pi}{6}$$
5*pi
t_2 = ----
6
$$t_{2} = \frac{5 \pi}{6}$$
Sum and product of roots
[src]
sum
pi 5*pi -- + ---- 6 6
$$\left(\frac{\pi}{6}\right) + \left(\frac{5 \pi}{6}\right)$$
=
pi
$$\pi$$
product
pi 5*pi -- * ---- 6 6
$$\left(\frac{\pi}{6}\right) * \left(\frac{5 \pi}{6}\right)$$
=
2 5*pi ----- 36
$$\frac{5 \pi^{2}}{36}$$
Numerical answer
[src]
t1 = -60.2138591938044
t2 = 69.6386371545737
t3 = 0.523598775598299
t4 = 59.1666616426078
t5 = -5.75958653158129
t6 = 50.789081233035
t7 = 34.0339204138894
t8 = -35.081117965086
t9 = -81.1578102177363
t10 = -74.8746249105567
t11 = 84.2994028713261
t12 = 78.0162175641465
t13 = -91.6297857297023
t14 = -79.0634151153431
t15 = -12.0427718387609
t16 = 134.564885328763
t17 = 6.80678408277789
t18 = 8.90117918517108
t19 = -2650.98060085419
t20 = 2.61799387799149
t21 = -87.4409955249159
t22 = -49.7418836818384
t23 = 94.7713783832921
t24 = 138.753675533549
t25 = -93.7241808320955
t26 = -53.9306738866248
t27 = -72.7802298081635
t28 = 82.2050077689329
t29 = -16.2315620435473
t30 = 40.317105721069
t31 = -24.60914245312
t32 = -56.025068989018
t33 = 15.1843644923507
t34 = 63.3554518473942
t35 = -28.7979326579064
t36 = -97.9129710368819
t37 = -68.5914396033772
t38 = 13.0899693899575
t39 = -30.8923277602996
t40 = -9.94837673636768
t41 = -47.6474885794452
t42 = 90.5825881785057
t43 = 27.7507351067098
t44 = 52.8834763354282
t45 = 71.733032256967
t46 = -627.79493194236
t47 = -41.3643032722656
t48 = 31.9395253114962
t49 = -22.5147473507269
t50 = -4454.25478401473
t51 = 38.2227106186758
t52 = 101.054563690472
t53 = -43.4586983746588
t54 = 17438.4572213013
t55 = 44.5058959258554
t56 = -3.66519142918809
t57 = -37.1755130674792
t58 = 19.3731546971371
t59 = 75.9218224617533
t60 = -18.3259571459405
t61 = 96.8657734856853
t62 = 88.4881930761125
t63 = 25.6563400043166
t64 = 21.4675497995303
t65 = 46.6002910282486
t66 = -62.3082542961976
t67 = -85.3466004225227
t68 = -100.007366139275
t69 = 57.0722665402146
t70 = -66.497044500984
t71 = 65.4498469497874
t71 = 65.4498469497874
The graph