Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation sin(x)+cos(x)=-1
-
Equation 3*9^(x-1/2)-7*6^x+3*4^(x+1)=0
-
Equation 13x+10=6x-4
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Equation (x-2)^4+3*(x-2)^2-10=0
- Express {x} in terms of y where:
- -4*x+6*y=-7
- 2*x+3*y=14
- -11*x+9*y=-20
- 10*x-18*y=-11
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Identical expressions
- sin(x)+sqrt((two -sqrt3)/ two *(cos(x)+ one))= zero
- sinus of (x) plus square root of ((2 minus square root of 3) divide by 2 multiply by ( co sinus of e of (x) plus 1)) equally 0
- sinus of (x) plus square root of ((two minus square root of 3) divide by two multiply by ( co sinus of e of (x) plus one)) equally zero
- sin(x)+√((2-√3)/2*(cos(x)+1))=0
- sin(x)+sqrt((2-sqrt3)/2(cos(x)+1))=0
- sinx+sqrt2-sqrt3/2cosx+1=0
- sin(x)+sqrt((2-sqrt3)/2*(cos(x)+1))=O
- sin(x)+sqrt((2-sqrt3) divide by 2*(cos(x)+1))=0
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Similar expressions
- sin(x)+sqrt((2+sqrt3)/2*(cos(x)+1))=0
- sin(x)-sqrt((2-sqrt3)/2*(cos(x)+1))=0
- sin(x)+sqrt((2-sqrt3)/2*(cos(x)-1))=0
- sinx+sqrt((2-sqrt3)/2*(cosx+1))=0
sin(x)+sqrt((2-sqrt3)/2*(cos(x)+1))=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
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________________________
/ ___
/ 2 - \/ 3
sin(x) + / ---------*(cos(x) + 1) = 0
\/ 2
$$\sqrt{\frac{2 - \sqrt{3}}{2} \left(\cos{\left(x \right)} + 1\right)} + \sin{\left(x \right)} = 0$$
Sum and product of roots
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sum
/ ___________\
| / ___ |
|\/ 2 - \/ 3 |
-2*atan|--------------|
| ___________|
| / ___ |
\\/ 2 + \/ 3 /
$$- 2 \operatorname{atan}{\left(\frac{\sqrt{2 - \sqrt{3}}}{\sqrt{\sqrt{3} + 2}} \right)}$$
=
/ ___________\
| / ___ |
|\/ 2 - \/ 3 |
-2*atan|--------------|
| ___________|
| / ___ |
\\/ 2 + \/ 3 /
$$- 2 \operatorname{atan}{\left(\frac{\sqrt{2 - \sqrt{3}}}{\sqrt{\sqrt{3} + 2}} \right)}$$
product
/ ___________\
| / ___ |
|\/ 2 - \/ 3 |
-2*atan|--------------|
| ___________|
| / ___ |
\\/ 2 + \/ 3 /
$$- 2 \operatorname{atan}{\left(\frac{\sqrt{2 - \sqrt{3}}}{\sqrt{\sqrt{3} + 2}} \right)}$$
=
/ ___________\
| / ___ |
|\/ 2 - \/ 3 |
-2*atan|--------------|
| ___________|
| / ___ |
\\/ 2 + \/ 3 /
$$- 2 \operatorname{atan}{\left(\frac{\sqrt{2 - \sqrt{3}}}{\sqrt{\sqrt{3} + 2}} \right)}$$
-2*atan(sqrt(2 - sqrt(3))/sqrt(2 + sqrt(3)))
Rapid solution
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/ ___________\
| / ___ |
|\/ 2 - \/ 3 |
x1 = -2*atan|--------------|
| ___________|
| / ___ |
\\/ 2 + \/ 3 /
$$x_{1} = - 2 \operatorname{atan}{\left(\frac{\sqrt{2 - \sqrt{3}}}{\sqrt{\sqrt{3} + 2}} \right)}$$
x1 = -2*atan(sqrt(2 - sqrt(3))/sqrt(sqrt(3) + 2))
Numerical answer
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x1 = -258.134196369961
x2 = -97.3893722612836
x3 = -72.2566310325652
x4 = 100.007366139275
x5 = -59.6902604182061
x6 = -13.0899693899575
x7 = -78.5398163397448
x8 = 30.8923277602996
x9 = 9.42477796076938
x10 = 97.3893722612836
x11 = -63.3554518473942
x12 = 84.8230016469244
x13 = -69.6386371545737
x14 = -25.6563400043166
x15 = -21.9911485751286
x16 = 12.0427718387609
x17 = 3.14159265358979
x18 = 18.3259571459405
x19 = 43.4586983746588
x20 = 28.2743338823081
x21 = -31.9395253114962
x22 = -28.2743338823081
x23 = -6.80678408277789
x24 = -40.8407044966673
x25 = -65.9734457253857
x26 = -91.106186954104
x27 = 24.60914245312
x28 = 219.387886975687
x29 = 5.75958653158129
x30 = -57.0722665402146
x31 = 40.8407044966673
x32 = -88.4881930761125
x33 = -14948.2214445558
x34 = -53.4070751110265
x35 = -3.14159265358979
x36 = -84.8230016469244
x37 = 21.9911485751286
x38 = -50.789081233035
x39 = 74.8746249105567
x40 = 34.5575191894877
x41 = 162.839219211071
x42 = 47.1238898038469
x43 = -15.707963267949
x44 = -101.054563690472
x45 = -75.9218224617533
x46 = 53.4070751110265
x47 = -19.3731546971371
x48 = 65.9734457253857
x49 = 93.7241808320955
x50 = 91.106186954104
x51 = 59.6902604182061
x52 = -44.5058959258554
x53 = -82.2050077689329
x54 = -0.523598775598299
x55 = 37.1755130674792
x56 = -94.7713783832921
x57 = 87.4409955249159
x58 = 78.5398163397448
x59 = 15.707963267949
x60 = 62.3082542961976
x61 = 72.2566310325652
x62 = 49.7418836818384
x63 = 56.025068989018
x64 = -47.1238898038469
x65 = -38.2227106186758
x66 = 81.1578102177363
x67 = -9.42477796076938
x68 = 68.5914396033772
x69 = -34.5575191894877
x69 = -34.5575191894877