Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation x^2+2*x+10=0
-
Equation 2^4-2*x=64
-
Equation x^2+3*x+9=0
- Equation x^2-x+30=0
- Express {x} in terms of y where:
- -18*x-3*y=2
- 5*x+20*y=-4
- 20*x-8*y=13
- -16*x+18*y=9
- Derivative of:
-
sin(x)
- Integral of d{x}:
-
sin(x)
- Canonical form:
- sin(x)
-
Identical expressions
- sin(x)=(- one)/sqrt(two)
- sinus of (x) equally ( minus 1) divide by square root of (2)
- sinus of (x) equally ( minus one) divide by square root of (two)
- sin(x)=(-1)/√(2)
- sinx=-1/sqrt2
- sin(x)=(-1) divide by sqrt(2)
-
Similar expressions
- sin(x)=(1)/sqrt(2)
- sinx=(-1)/sqrt(2)
sin(x)=(-1)/sqrt(2) equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$\sin{\left(x \right)} = - \frac{1}{\sqrt{2}}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$x = 2 \pi n + \operatorname{asin}{\left(- \frac{\sqrt{2}}{2} \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(- \frac{\sqrt{2}}{2} \right)} + \pi$$
Or
$$x = 2 \pi n - \frac{\pi}{4}$$
$$x = 2 \pi n + \frac{5 \pi}{4}$$
, where n - is a integer
$$\sin{\left(x \right)} = - \frac{1}{\sqrt{2}}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$x = 2 \pi n + \operatorname{asin}{\left(- \frac{\sqrt{2}}{2} \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(- \frac{\sqrt{2}}{2} \right)} + \pi$$
Or
$$x = 2 \pi n - \frac{\pi}{4}$$
$$x = 2 \pi n + \frac{5 \pi}{4}$$
, where n - is a integer
Sum and product of roots
[src]
sum
pi 5*pi - -- + ---- 4 4
$$- \frac{\pi}{4} + \frac{5 \pi}{4}$$
=
pi
$$\pi$$
product
-pi 5*pi ----*---- 4 4
$$- \frac{\pi}{4} \frac{5 \pi}{4}$$
=
2 -5*pi ------ 16
$$- \frac{5 \pi^{2}}{16}$$
-5*pi^2/16
Rapid solution
[src]
-pi
x1 = ----
4
$$x_{1} = - \frac{\pi}{4}$$
5*pi
x2 = ----
4
$$x_{2} = \frac{5 \pi}{4}$$
x2 = 5*pi/4
Numerical answer
[src]
x1 = -40.0553063332699
x2 = -128.019900633784
x3 = 652.665873783279
x4 = 85.6083998103219
x5 = -704.502152567511
x6 = -13.3517687777566
x7 = -371.493331286993
x8 = -63.6172512351933
x9 = 68.329640215578
x10 = -44.7676953136546
x11 = -27.4889357189107
x12 = -14.9225651045515
x13 = -101.316363078271
x14 = 66.7588438887831
x15 = 49.4800842940392
x16 = -8.63937979737193
x17 = 24.3473430653209
x18 = -46.3384916404494
x19 = 36.9137136796801
x20 = 30.6305283725005
x21 = 5.49778714378214
x22 = 43.1968989868597
x23 = 11.7809724509617
x24 = -57.3340659280137
x25 = -71.4712328691678
x26 = 3.92699081698724
x27 = -51.0508806208341
x28 = 73.0420291959627
x29 = 54.1924732744239
x30 = -830.165858711103
x31 = 99.7455667514759
x32 = -21.2057504117311
x33 = 16.4933614313464
x34 = -65.1880475619882
x35 = 60.4756585816035
x36 = 80.8960108299372
x37 = -95.0331777710912
x38 = -69.9004365423729
x39 = 29.0597320457056
x40 = 10.2101761241668
x41 = -7.06858347057703
x42 = 87.1791961371168
x43 = -32.2013246992954
x44 = -25.9181393921158
x45 = 41.6261026600648
x46 = 74.6128255227576
x47 = 93.4623814442964
x48 = -2865.91789823729
x49 = -2.35619449019234
x50 = -96.6039740978861
x51 = -82.4668071567321
x52 = 98.174770424681
x53 = -58.9048622548086
x54 = -52.621676947629
x55 = 35.3429173528852
x56 = -84.037603483527
x57 = 18.0641577581413
x58 = 55.7632696012188
x59 = -215482.625507887
x60 = -0.785398163397448
x61 = 22.776546738526
x62 = -77.7544181763474
x63 = -90.3207887907066
x64 = -33.7721210260903
x65 = 62.0464549083984
x66 = -38.484510006475
x67 = -88.7499924639117
x68 = -76.1836218495525
x69 = 79.3252145031423
x70 = -19.6349540849362
x71 = 47.9092879672443
x72 = 91.8915851175014
x72 = 91.8915851175014
The graph