Mister Exam
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How to use it?
- Equation:
-
Equation 14x-25=20x+9
-
Equation (x-5)^2=(x+15)^2
- Equation log(x-7)25=2
- Equation ((8z-1)/5)-((3z+3)/4)=((50-2z)/9)+1
- Express {x} in terms of y where:
- 9*x-8*y=6
- 15*x+15*y=16
- 8*x+7*y=-13
- -4*x+18*y=-14
-
Identical expressions
- (five *cos(x)- three)/(three *tg(x)+ four)= zero
- (5 multiply by co sinus of e of (x) minus 3) divide by (3 multiply by tg(x) plus 4) equally 0
- (five multiply by co sinus of e of (x) minus three) divide by (three multiply by tg(x) plus four) equally zero
- (5cos(x)-3)/(3tg(x)+4)=0
- 5cosx-3/3tgx+4=0
- (5*cos(x)-3)/(3*tg(x)+4)=O
- (5*cos(x)-3) divide by (3*tg(x)+4)=0
-
Similar expressions
- (5*cos(x)+3)/(3*tg(x)+4)=0
- (5*cos(x)-3)/(3*tg(x)-4)=0
- (5*cosx-3)/(3*tg(x)+4)=0
(5*cos(x)-3)/(3*tg(x)+4)=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
5*cos(x) - 3 ------------ = 0 3*tan(x) + 4
$$\frac{5 \cos{\left(x \right)} - 3}{3 \tan{\left(x \right)} + 4} = 0$$
Detail solution
Given the equation
$$\frac{5 \cos{\left(x \right)} - 3}{3 \tan{\left(x \right)} + 4} = 0$$
transform
$$\frac{5 \cos{\left(x \right)} - 3}{3 \tan{\left(x \right)} + 4} = 0$$
$$\frac{5 \cos{\left(x \right)} - 3}{3 \tan{\left(x \right)} + 4} = 0$$
Do replacement
$$w = \tan{\left(x \right)}$$
Given the equation:
$$\frac{5 \cos{\left(x \right)} - 3}{3 w + 4} = 0$$
Multiply the equation sides by the denominator 4 + 3*w
we get:
$$5 \cos{\left(x \right)} - 3 = 0$$
Expand brackets in the left part
Move free summands (without w)
from left part to right part, we given:
$$5 \cos{\left(x \right)} = 3$$
This equation has no roots
do backward replacement
$$\tan{\left(x \right)} = w$$
Given the equation
$$\tan{\left(x \right)} = w$$
- this is the simplest trigonometric equation
This equation is transformed to
$$x = \pi n + \operatorname{atan}{\left(w \right)}$$
Or
$$x = \pi n + \operatorname{atan}{\left(w \right)}$$
, where n - is a integer
substitute w:
$$\frac{5 \cos{\left(x \right)} - 3}{3 \tan{\left(x \right)} + 4} = 0$$
transform
$$\frac{5 \cos{\left(x \right)} - 3}{3 \tan{\left(x \right)} + 4} = 0$$
$$\frac{5 \cos{\left(x \right)} - 3}{3 \tan{\left(x \right)} + 4} = 0$$
Do replacement
$$w = \tan{\left(x \right)}$$
Given the equation:
$$\frac{5 \cos{\left(x \right)} - 3}{3 w + 4} = 0$$
Multiply the equation sides by the denominator 4 + 3*w
we get:
$$5 \cos{\left(x \right)} - 3 = 0$$
Expand brackets in the left part
-3 + 5*cosx = 0
Move free summands (without w)
from left part to right part, we given:
$$5 \cos{\left(x \right)} = 3$$
This equation has no roots
do backward replacement
$$\tan{\left(x \right)} = w$$
Given the equation
$$\tan{\left(x \right)} = w$$
- this is the simplest trigonometric equation
This equation is transformed to
$$x = \pi n + \operatorname{atan}{\left(w \right)}$$
Or
$$x = \pi n + \operatorname{atan}{\left(w \right)}$$
, where n - is a integer
substitute w:
Sum and product of roots
[src]
sum
acos(3/5)
$$\operatorname{acos}{\left(\frac{3}{5} \right)}$$
=
acos(3/5)
$$\operatorname{acos}{\left(\frac{3}{5} \right)}$$
product
acos(3/5)
$$\operatorname{acos}{\left(\frac{3}{5} \right)}$$
=
acos(3/5)
$$\operatorname{acos}{\left(\frac{3}{5} \right)}$$
acos(3/5)
Rapid solution
[src]
x1 = acos(3/5)
$$x_{1} = \operatorname{acos}{\left(\frac{3}{5} \right)}$$
x1 = acos(3/5)
Numerical answer
[src]
x1 = 82.6087042113362
x2 = -143.585966847129
x3 = -1.5707963267949
x4 = -93.3204843896922
x5 = -64.4026493985908
x6 = 80.1106126665397
x7 = -48.6946861306418
x8 = -58.1194640914112
x9 = 61.261056745001
x10 = 88.8918895185158
x11 = -112.170040311231
x12 = -29.845130209103
x13 = 38.6264070610791
x14 = -99.6036696968718
x15 = -49.3381872394351
x16 = -11.6390753963576
x17 = -61.9045578537943
x18 = -86.3937979737193
x19 = -36.1283155162826
x20 = 114.024630747234
x21 = 1.5707963267949
x22 = -39.2699081698724
x23 = 73.8274273593601
x24 = 42.4115008234622
x25 = 67.5442420521806
x26 = -68.1877431609738
x27 = -32.9867228626928
x28 = 14.1371669411541
x29 = -80.754113775333
x30 = 4.71238898038469
x31 = 44.9095923682587
x32 = 36.1283155162826
x33 = -70.6858347057703
x34 = -26.7035375555132
x35 = 10.9955742875643
x36 = 26.06003644672
x37 = 23.5619449019235
x38 = 45.553093477052
x39 = 95.8185759344887
x40 = -89.5353906273091
x41 = -5.35589008917797
x42 = -24.2054460107167
x43 = 17.2787595947439
x44 = -42.4115008234622
x45 = 54.9778714378214
x46 = -7.85398163397448
x47 = -55.6213725466147
x48 = 48.6946861306418
x49 = -17.9222607035371
x50 = 89.5353906273091
x51 = 0.927295218001612
x52 = -51.8362787842316
x53 = 92.6769832808989
x54 = 58.1194640914112
x55 = -73.8274273593601
x56 = 86.3937979737193
x57 = -76.9690200129499
x58 = 19.7768511395404
x59 = -80.1106126665397
x60 = 51.8362787842316
x61 = -43.0550019322555
x62 = -20.4203522483337
x63 = 64.4026493985908
x64 = 76.3255189041567
x65 = -83.2522053201295
x66 = 32.3432217538995
x67 = 98.9601685880785
x68 = 7.85398163397448
x69 = 70.0423335969771
x70 = -14.1371669411541
x71 = -95.8185759344887
x72 = 29.845130209103
x73 = -45.553093477052
x74 = -87.0372990825126
x74 = -87.0372990825126