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- Equation:
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Equation cos2x-1=0
- Equation 3sin^2(3x)-2,5sin(6x)+1=0
- Equation cos((Pi/9)-4x)=1
- Equation (4x-3)(4x+3)=0
- Express {x} in terms of y where:
- -14*x-1*y=3
- 8*x+7*y=-13
- 5*x+5*y=20
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Identical expressions
- cos((Pi/ nine)-4x)= one
- co sinus of e of ((Pi divide by 9) minus 4x) equally 1
- co sinus of e of ((Pi divide by nine) minus 4x) equally one
- cosPi/9-4x=1
- cos((Pi divide by 9)-4x)=1
-
Similar expressions
- cos((Pi/9)+4x)=1
cos((Pi/9)-4x)=1 equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
/pi \ cos|-- - 4*x| = 1 \9 /
$$\cos{\left(- 4 x + \frac{\pi}{9} \right)} = 1$$
Detail solution
Given the equation
$$\cos{\left(- 4 x + \frac{\pi}{9} \right)} = 1$$
- this is the simplest trigonometric equation
This equation is transformed to
$$4 x + \frac{7 \pi}{18} = 2 \pi n + \operatorname{asin}{\left(1 \right)}$$
$$4 x + \frac{7 \pi}{18} = 2 \pi n - \operatorname{asin}{\left(1 \right)} + \pi$$
Or
$$4 x + \frac{7 \pi}{18} = 2 \pi n + \frac{\pi}{2}$$
$$4 x + \frac{7 \pi}{18} = 2 \pi n + \frac{\pi}{2}$$
, where n - is a integer
Move
$$\frac{7 \pi}{18}$$
to right part of the equation
with the opposite sign, in total:
$$4 x = 2 \pi n + \frac{\pi}{9}$$
$$4 x = 2 \pi n + \frac{\pi}{9}$$
Divide both parts of the equation by
$$4$$
we get the answer:
$$x_{1} = \frac{\pi n}{2} + \frac{\pi}{36}$$
$$x_{2} = \frac{\pi n}{2} + \frac{\pi}{36}$$
$$\cos{\left(- 4 x + \frac{\pi}{9} \right)} = 1$$
- this is the simplest trigonometric equation
This equation is transformed to
$$4 x + \frac{7 \pi}{18} = 2 \pi n + \operatorname{asin}{\left(1 \right)}$$
$$4 x + \frac{7 \pi}{18} = 2 \pi n - \operatorname{asin}{\left(1 \right)} + \pi$$
Or
$$4 x + \frac{7 \pi}{18} = 2 \pi n + \frac{\pi}{2}$$
$$4 x + \frac{7 \pi}{18} = 2 \pi n + \frac{\pi}{2}$$
, where n - is a integer
Move
$$\frac{7 \pi}{18}$$
to right part of the equation
with the opposite sign, in total:
$$4 x = 2 \pi n + \frac{\pi}{9}$$
$$4 x = 2 \pi n + \frac{\pi}{9}$$
Divide both parts of the equation by
$$4$$
we get the answer:
$$x_{1} = \frac{\pi n}{2} + \frac{\pi}{36}$$
$$x_{2} = \frac{\pi n}{2} + \frac{\pi}{36}$$
Sum and product of roots
[src]
sum
pi -- 36
$$\frac{\pi}{36}$$
=
pi -- 36
$$\frac{\pi}{36}$$
product
pi -- 36
$$\frac{\pi}{36}$$
=
pi -- 36
$$\frac{\pi}{36}$$
pi/36
Numerical answer
[src]
x1 = -12.4791042131093
x2 = 37.7863784216865
x3 = 78.6270826988203
x4 = 0.0872667782384371
x5 = -53.3198087067381
x6 = 42.4987671739903
x7 = 15.7952298446077
x8 = 34.6447855586004
x9 = 81.7686755752369
x10 = 72.3438974380663
x11 = -80.0233461796468
x12 = 95.9058424699032
x13 = -72.1693648950812
x14 = 45.6403600519256
x15 = -28.1870673101421
x16 = 92.7642500048763
x17 = 14.2244334242509
x18 = -86.3065313879892
x19 = -7.76671515834831
x20 = 56.6359341282408
x21 = 67.6315086235637
x22 = 28.361600279185
x23 = 86.4810643279505
x24 = 80.197879175411
x25 = 6.37045169996086
x26 = -72.1693644656717
x27 = 51.9235453097555
x28 = 29.9323967292291
x29 = 73.9146938899713
x30 = -20.3330856661766
x31 = -34.4702527562253
x32 = 75.4854898875476
x33 = -14.049900432901
x34 = -59.602994036852
x35 = 97.4766384139647
x36 = -56.4614013050312
x37 = -15.6206968791201
x38 = 12.6536369900585
x39 = 94.3350460177276
x40 = -94.1605130437285
x41 = -95.7313094851324
x42 = 53.4943413718914
x43 = -75.3109572683443
x44 = -9.33751157718683
x45 = 88.0518606536713
x46 = 44.0695634005613
x47 = 50.3527488585529
x48 = -97.3021058272143
x49 = -100.443698415653
x50 = 58.2067305910165
x51 = -81.5941426155007
x52 = 64.4899157508705
x53 = -37.611845458058
x54 = 22.0784149665373
x55 = -45.465827131301
x56 = 48.7819528362493
x57 = 70.7731014780795
x58 = -1.48352997912758
x59 = -42.3242342397544
x60 = -12.4791042029249
x61 = 100.618231270209
x62 = -78.452549858469
x63 = -6.19591873266924
x64 = 7.94124814835801
x65 = -29.7578637405335
x66 = 66.0607120362936
x67 = 23.6492114797134
x68 = 36.2155820073397
x69 = -58.0321975968207
x70 = 20.5076185973203
x71 = -67.4569757069933
x72 = -43.8950303690659
x73 = -51.7490123223636
x74 = 1.65806290699436
x75 = 9.5120443231479
x76 = -89.4481242823959
x77 = -50.1782158878097
x78 = -31.3286601428889
x79 = -50.1782159947367
x80 = -64.3153828137022
x81 = 89.6226571945447
x82 = -23.4746785553399
x83 = -36.0410490146034
x84 = -73.7401609038844
x85 = 31.5031928515163
x86 = 59.7775269985642
x86 = 59.7775269985642