Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation cos(x)-1=0
- Equation 64-x^2=0
-
Equation sin(5*x)=-1
-
Equation cos(x/2)=-1
- Express {x} in terms of y where:
- 10*x-15*y=-2
- 16*x-9*y=4
- -9*x-20*y=14
- 13*x+12*y=-18
- Graphing y =:
- sin(5*x)
- Integral of d{x}:
-
sin(5*x)
-
-1
- Derivative of:
-
sin(5*x)
-
-1
- Sum of series:
-
-1
-
Identical expressions
- sin(five *x)=- one
- sinus of (5 multiply by x) equally minus 1
- sinus of (five multiply by x) equally minus one
- sin(5x)=-1
- sin5x=-1
-
Similar expressions
- sin(5*x)=+1
- sin5(x)=-sin(x)
- sin(5x/3)+sin(3x/2)=0
sin(5*x)=-1 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$\sin{\left(5 x \right)} = -1$$
- this is the simplest trigonometric equation
This equation is transformed to
$$5 x = 2 \pi n + \operatorname{asin}{\left(-1 \right)}$$
$$5 x = 2 \pi n - \operatorname{asin}{\left(-1 \right)} + \pi$$
Or
$$5 x = 2 \pi n - \frac{\pi}{2}$$
$$5 x = 2 \pi n + \frac{3 \pi}{2}$$
, where n - is a integer
Divide both parts of the equation by
$$5$$
we get the answer:
$$x_{1} = \frac{2 \pi n}{5} - \frac{\pi}{10}$$
$$x_{2} = \frac{2 \pi n}{5} + \frac{3 \pi}{10}$$
$$\sin{\left(5 x \right)} = -1$$
- this is the simplest trigonometric equation
This equation is transformed to
$$5 x = 2 \pi n + \operatorname{asin}{\left(-1 \right)}$$
$$5 x = 2 \pi n - \operatorname{asin}{\left(-1 \right)} + \pi$$
Or
$$5 x = 2 \pi n - \frac{\pi}{2}$$
$$5 x = 2 \pi n + \frac{3 \pi}{2}$$
, where n - is a integer
Divide both parts of the equation by
$$5$$
we get the answer:
$$x_{1} = \frac{2 \pi n}{5} - \frac{\pi}{10}$$
$$x_{2} = \frac{2 \pi n}{5} + \frac{3 \pi}{10}$$
Rapid solution
[src]
-pi
x1 = ----
10
$$x_{1} = - \frac{\pi}{10}$$
3*pi
x2 = ----
10
$$x_{2} = \frac{3 \pi}{10}$$
x2 = 3*pi/10
Sum and product of roots
[src]
sum
pi 3*pi - -- + ---- 10 10
$$- \frac{\pi}{10} + \frac{3 \pi}{10}$$
=
pi -- 5
$$\frac{\pi}{5}$$
product
-pi 3*pi ----*---- 10 10
$$- \frac{\pi}{10} \frac{3 \pi}{10}$$
=
2 -3*pi ------ 100
$$- \frac{3 \pi^{2}}{100}$$
-3*pi^2/100
Numerical answer
[src]
x1 = -45.5530935651178
x2 = -75.7123829768599
x3 = -51.8362786929109
x4 = 76.3407014282439
x5 = 72.570790252592
x6 = 5.96902607240456
x7 = -92.0486647063443
x8 = 97.703531597323
x9 = 52.4645972249968
x10 = 56.2345085113038
x11 = -98.3318500297616
x12 = -4.08407038508313
x13 = -34.2433598309698
x14 = -7.85398151412802
x15 = 2.19911490246744
x16 = -69.42919768965
x17 = -25.4469005589667
x18 = -99.588487199358
x19 = -27.9601746876698
x20 = -58.1194640118314
x21 = -0.314159211507129
x22 = -4.0840703117445
x23 = -81.9955682642019
x24 = -65.6592865140204
x25 = -61.8893749736422
x26 = 33.6150412025629
x27 = 12.2522113473678
x28 = 5.96902610606135
x29 = 93.933620397379
x30 = 77.5973383555507
x31 = -21.6769893550399
x32 = 62.5176937218139
x33 = 82.6238869092536
x34 = -35.4999970742626
x35 = -64.4026495871078
x36 = 18.5353965790101
x37 = -24.1902633373992
x38 = -15.3938039659798
x39 = -41.7831822653761
x40 = 70.0575160400951
x41 = -31.7300858152792
x42 = -95.8185758687136
x43 = 46.1814120735606
x44 = 19.7920338136899
x45 = 29.8451302988705
x46 = -11.6238928872839
x47 = -68.1725604897886
x48 = 49.9513232359226
x49 = 86.393797898483
x50 = 38.6415898747305
x51 = -71.942471902222
x52 = 96.4468943771426
x53 = -54.3495529216771
x54 = 73.827427452472
x55 = 42.411500742904
x56 = 53.721234458049
x57 = 83.8805239304316
x58 = 100.216805676894
x59 = 63.7743309633316
x60 = 16.0221225012125
x61 = -85.7654794309647
x62 = -88.2787534842036
x63 = -10.3672558405688
x64 = 32.3584042700694
x65 = 60.0044196780723
x66 = 39.8982267733088
x67 = -278.030949800724
x68 = -78.2256569789261
x69 = -79.482294220441
x70 = 26.0752188396735
x71 = 9.73893731490784
x72 = -59.376101032934
x73 = -22.9336264075169
x74 = 22.3053078047562
x75 = -89.5353907172626
x76 = 66.2876049654061
x77 = -38.0132710938785
x78 = -55.6061900437796
x79 = 80.1106129684713
x80 = -1.57079641167075
x81 = -48.0663675448867
x82 = 43.6681379124747
x83 = 28.5884931335501
x84 = 90.163709249367
x85 = -14.1371668558998
x86 = -44.2964563449265
x87 = 87.6504350205451
x88 = 8.48230007440474
x88 = 8.48230007440474
The graph