Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation (x-7)^2=(9-x)^2
-
Equation z^4+1=0
-
Equation sin(x)=3/4
- Equation lg(x-1)+lg(x-1)=0
- Express {x} in terms of y where:
- -14*x-3*y=-5
- -7*x-13*y=5
- 9*x-17*y=13
- 4*x+15*y=19
- Integral of d{x}:
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sint
- Derivative of:
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sint
-
Identical expressions
- sint=- zero . two
- sinus of t equally minus 0.2
- sinus of t equally minus zero . two
-
Similar expressions
- y=c^1*e^t*sin(t)
- sin(t)=-sqrt(3)
- sint=+0.2
- 2sin(t)=1
sint=-0.2 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$\sin{\left(t \right)} = - \frac{1}{5}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$t = 2 \pi n + \operatorname{asin}{\left(- \frac{1}{5} \right)}$$
$$t = 2 \pi n - \operatorname{asin}{\left(- \frac{1}{5} \right)} + \pi$$
Or
$$t = 2 \pi n - \operatorname{asin}{\left(\frac{1}{5} \right)}$$
$$t = 2 \pi n + \operatorname{asin}{\left(\frac{1}{5} \right)} + \pi$$
, where n - is a integer
$$\sin{\left(t \right)} = - \frac{1}{5}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$t = 2 \pi n + \operatorname{asin}{\left(- \frac{1}{5} \right)}$$
$$t = 2 \pi n - \operatorname{asin}{\left(- \frac{1}{5} \right)} + \pi$$
Or
$$t = 2 \pi n - \operatorname{asin}{\left(\frac{1}{5} \right)}$$
$$t = 2 \pi n + \operatorname{asin}{\left(\frac{1}{5} \right)} + \pi$$
, where n - is a integer
Sum and product of roots
[src]
sum
pi + asin(1/5) - asin(1/5)
$$- \operatorname{asin}{\left(\frac{1}{5} \right)} + \left(\operatorname{asin}{\left(\frac{1}{5} \right)} + \pi\right)$$
=
pi
$$\pi$$
product
(pi + asin(1/5))*(-asin(1/5))
$$\left(\operatorname{asin}{\left(\frac{1}{5} \right)} + \pi\right) \left(- \operatorname{asin}{\left(\frac{1}{5} \right)}\right)$$
=
-(pi + asin(1/5))*asin(1/5)
$$- \left(\operatorname{asin}{\left(\frac{1}{5} \right)} + \pi\right) \operatorname{asin}{\left(\frac{1}{5} \right)}$$
-(pi + asin(1/5))*asin(1/5)
Rapid solution
[src]
t1 = pi + asin(1/5)
$$t_{1} = \operatorname{asin}{\left(\frac{1}{5} \right)} + \pi$$
t2 = -asin(1/5)
$$t_{2} = - \operatorname{asin}{\left(\frac{1}{5} \right)}$$
t2 = -asin(1/5)
Numerical answer
[src]
t1 = 41.0420624174576
t2 = 129.006656717972
t3 = 68.9136804581851
t4 = 15.9093211887393
t5 = -9.22342003997905
t6 = -0.201357920790331
t7 = -21.7897906543382
t8 = -69.3163962997658
t9 = 24.931383307928
t10 = 81.4800510725443
t11 = 59.8916183389964
t12 = 47.3252477246372
t13 = -75.5995816069454
t14 = 53.6084330318168
t15 = -15.5066053471586
t16 = 78.7411742605352
t17 = -88.1659522213045
t18 = 56.3473098438259
t19 = -37.9004697638678
t20 = 91.3075448748943
t21 = 37.4977539222872
t22 = 85.0243595677148
t23 = -40.639346575877
t24 = 9.62613588155971
t25 = 87.7632363797239
t26 = 4024.58154716932
t27 = -63.0332109925862
t28 = -50.466840378227
t29 = 34.7588771102781
t30 = 172.988953868229
t31 = 28.4756918030985
t32 = -94.4491375284841
t33 = 97.5907301820739
t34 = -78.3384584189545
t35 = 3845.10805007312
t36 = 66.174803646176
t37 = 22.1925064959189
t38 = 6.08182738638926
t39 = -84.6216437261341
t40 = 75.1968657653647
t41 = 18.6481980007484
t42 = -46.9225318830566
t43 = -56.7500256854066
t44 = 94.0464216869035
t45 = -6.48454322796992
t46 = -72.0552731117749
t47 = -19.0509138423291
t48 = 225.993313137675
t49 = 50.0641245366464
t50 = -65.7720878045953
t51 = -107.015508142843
t52 = 62.6304951510055
t53 = 72.4579889533556
t54 = 3.34295057438012
t55 = -279.400388248701
t56 = 9845.55001842962
t57 = -97.1880143404933
t58 = -59.4889024974157
t59 = -25.3340991495087
t60 = 43.7809392294668
t61 = -34.3561612686974
t62 = 100.329606994083
t63 = -2.94023473279946
t64 = -12.7677285351495
t65 = 31.2145686151076
t66 = -53.2057171902362
t67 = 12.3650126935688
t68 = -28.0729759615178
t69 = -100.732322835664
t70 = -44.1836550710474
t71 = -81.882766914125
t72 = -90.9048290333137
t73 = -31.6172844566883
t73 = -31.6172844566883