Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation (x+6)(2x+6)-20=0
- Equation arctg(x/y)
-
Equation sinx=1/3
- Equation 20450x^2-36*x-10800=0
- Express {x} in terms of y where:
- -10*x+18*y=6
- 9*x-18*y=6
- -1*x+19*y=-10
- 4*x+13*y=13
- Integral of d{x}:
-
sint
- Derivative of:
-
sint
-
Identical expressions
- sint=-sqrt3/ two
- sinus of t equally minus square root of 3 divide by 2
- sinus of t equally minus square root of 3 divide by two
- sint=-√3/2
- sint=-sqrt3 divide by 2
-
Similar expressions
- 4sqrt((1-((sqrt(3))/2))/(6x+6))+pi/(6x+6)=1,5*sqrt(3)-2
- sin(x)+sqrt(((2-sqrt(3))/2)(cos(x)+1))=0
- cos(x)=-sqrt(3)/2
- (sin(x)-(sqrt(3)/2))*sqrt(3*x^2-7*x+4)=0
- sin(t)=1/3
- sint=+sqrt3/2
- -4*(2*cos(t)-(3/2))*sin(t)+2*sin(t*cos(t))=0
sint=-sqrt3/2 equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
___
-\/ 3
sin(t) = -------
2
$$\sin{\left(t \right)} = \frac{\left(-1\right) \sqrt{3}}{2}$$
Detail solution
Given the equation
$$\sin{\left(t \right)} = \frac{\left(-1\right) \sqrt{3}}{2}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$t = 2 \pi n + \operatorname{asin}{\left(- \frac{\sqrt{3}}{2} \right)}$$
$$t = 2 \pi n - \operatorname{asin}{\left(- \frac{\sqrt{3}}{2} \right)} + \pi$$
Or
$$t = 2 \pi n - \frac{\pi}{3}$$
$$t = 2 \pi n + \frac{4 \pi}{3}$$
, where n - is a integer
$$\sin{\left(t \right)} = \frac{\left(-1\right) \sqrt{3}}{2}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$t = 2 \pi n + \operatorname{asin}{\left(- \frac{\sqrt{3}}{2} \right)}$$
$$t = 2 \pi n - \operatorname{asin}{\left(- \frac{\sqrt{3}}{2} \right)} + \pi$$
Or
$$t = 2 \pi n - \frac{\pi}{3}$$
$$t = 2 \pi n + \frac{4 \pi}{3}$$
, where n - is a integer
Sum and product of roots
[src]
sum
pi 4*pi - -- + ---- 3 3
$$- \frac{\pi}{3} + \frac{4 \pi}{3}$$
=
pi
$$\pi$$
product
-pi 4*pi ----*---- 3 3
$$- \frac{\pi}{3} \frac{4 \pi}{3}$$
=
2 -4*pi ------ 9
$$- \frac{4 \pi^{2}}{9}$$
-4*pi^2/9
Rapid solution
[src]
-pi
t1 = ----
3
$$t_{1} = - \frac{\pi}{3}$$
4*pi
t2 = ----
3
$$t_{2} = \frac{4 \pi}{3}$$
t2 = 4*pi/3
Numerical answer
[src]
t1 = 11.5191730631626
t2 = 99.4837673636768
t3 = -114.144533080429
t4 = -5606.69568910658
t5 = -1.0471975511966
t6 = -101.57816246607
t7 = -14.6607657167524
t8 = -89.0117918517108
t9 = -33.5103216382911
t10 = 30.3687289847013
t11 = -46.0766922526503
t12 = -64.9262481741891
t13 = -32.4631240870945
t14 = -38.7463093942741
t15 = 36.6519142918809
t16 = -52.3598775598299
t17 = 93.2005820564972
t18 = -27.2271363311115
t19 = -90.0589894029074
t20 = -151.843644923507
t21 = -8.37758040957278
t22 = 55.5014702134197
t23 = 74.3510261349584
t24 = -96.342174710087
t25 = 17.8023583703422
t26 = 85.870199198121
t27 = -51.3126800086333
t28 = 10.471975511966
t29 = -57.5958653158129
t30 = 60.7374579694027
t31 = -82.7286065445312
t32 = 79.5870138909414
t33 = -77.4926187885482
t34 = -39.7935069454707
t35 = 24.0855436775217
t36 = 86.9173967493176
t37 = 35.6047167406843
t38 = -83.7758040957278
t39 = 41.8879020478639
t40 = 92.1533845053006
t41 = -26.1799387799149
t42 = -58.6430628670095
t43 = 73.3038285837618
t44 = 5.23598775598299
t45 = 49.2182849062401
t46 = 48.1710873550435
t47 = -70.162235930172
t48 = -11851.1346868919
t49 = 29.3215314335047
t50 = -2.0943951023932
t51 = 16.7551608191456
t52 = 54.4542726622231
t53 = 80.634211442138
t54 = -95.2949771588904
t55 = -13.6135681655558
t56 = 61.7846555205993
t57 = 67.0206432765823
t58 = 98.4365698124802
t59 = 23.0383461263252
t60 = -76.4454212373516
t61 = -63.8790506229925
t62 = 42.9350995990605
t63 = 68.0678408277789
t64 = -20.943951023932
t65 = -7.33038285837618
t66 = -1559.27715373173
t67 = -45.0294947014537
t68 = -19.8967534727354
t69 = 393.746279249921
t70 = -71.2094334813686
t71 = 4.18879020478639
t71 = 4.18879020478639