Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation 9(x-1)=x+15
-
Equation sin(x/3)=1/2
-
Equation x^2=12
-
Equation 8*x=2
- Express {x} in terms of y where:
- 10*x-2*y=11
- 11*x-2*y=-9
- 4*x+18*y=-7
- 7*x+6*y=20
-
Identical expressions
- 2sin(t)= one
- 2 sinus of (t) equally 1
- 2 sinus of (t) equally one
- 2sint=1
-
Similar expressions
- x.diff(x)=(2*sin(t))*x+(log(t))*y
- (cos(t)+2)*3*k-2*sin(t)=0
- (-12*sin(t))/t+6*cos(t)+t*t=2*(b*sin(t)+3*cos(t))
2sin(t)=1 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$2 \sin{\left(t \right)} = 1$$
- this is the simplest trigonometric equation
The equation is transformed to
$$\sin{\left(t \right)} = \frac{1}{2}$$
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
$$2 \sin{\left(t \right)} = 1$$
- this is the simplest trigonometric equation
Divide both parts of the equation by 2
The equation is transformed to
$$\sin{\left(t \right)} = \frac{1}{2}$$
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
t1 = --
6
$$t_{1} = \frac{\pi}{6}$$
5*pi
t2 = ----
6
$$t_{2} = \frac{5 \pi}{6}$$
t2 = 5*pi/6
Sum and product of roots
[src]
sum
pi 5*pi -- + ---- 6 6
$$\frac{\pi}{6} + \frac{5 \pi}{6}$$
=
pi
$$\pi$$
product
pi 5*pi --*---- 6 6
$$\frac{\pi}{6} \frac{5 \pi}{6}$$
=
2 5*pi ----- 36
$$\frac{5 \pi^{2}}{36}$$
5*pi^2/36
Numerical answer
[src]
t1 = 25.6563400043166
t2 = -62.3082542961976
t3 = -74.8746249105567
t4 = 138.753675533549
t5 = -81.1578102177363
t6 = -53.9306738866248
t7 = -49.7418836818384
t8 = 15.1843644923507
t9 = -97.9129710368819
t10 = 82.2050077689329
t11 = -5.75958653158129
t12 = -100.007366139275
t13 = -22.5147473507269
t14 = -37.1755130674792
t15 = -66.497044500984
t16 = 88.4881930761125
t17 = -3.66519142918809
t18 = 31.9395253114962
t19 = -72.7802298081635
t20 = -4454.25478401473
t21 = 78.0162175641465
t22 = 19.3731546971371
t23 = -87.4409955249159
t24 = 50.789081233035
t25 = -24.60914245312
t26 = 40.317105721069
t27 = -30.8923277602996
t28 = 84.2994028713261
t29 = -79.0634151153431
t30 = 96.8657734856853
t31 = 101.054563690472
t32 = 59.1666616426078
t33 = 27.7507351067098
t34 = -16.2315620435473
t35 = -85.3466004225227
t36 = 17438.4572213013
t37 = 52.8834763354282
t38 = 63.3554518473942
t39 = -47.6474885794452
t40 = 90.5825881785057
t41 = -2650.98060085419
t42 = 34.0339204138894
t43 = 57.0722665402146
t44 = 8.90117918517108
t45 = 21.4675497995303
t46 = 44.5058959258554
t47 = 13.0899693899575
t48 = -68.5914396033772
t49 = 65.4498469497874
t50 = -35.081117965086
t51 = 46.6002910282486
t52 = 134.564885328763
t53 = 0.523598775598299
t54 = -41.3643032722656
t55 = -12.0427718387609
t56 = 6.80678408277789
t57 = 38.2227106186758
t58 = -60.2138591938044
t59 = -627.79493194236
t60 = -43.4586983746588
t61 = -93.7241808320955
t62 = 2.61799387799149
t63 = 69.6386371545737
t64 = -18.3259571459405
t65 = -28.7979326579064
t66 = 75.9218224617533
t67 = -56.025068989018
t68 = -91.6297857297023
t69 = -9.94837673636768
t70 = 71.733032256967
t71 = 94.7713783832921
t71 = 94.7713783832921