Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation 4x-x^2=x^2-x+3
-
Equation 3*x^2-x-5=0
-
Equation x^6=-64
-
Equation x^2-21=4x
- Express {x} in terms of y where:
- 12*x+6*y=-5
- -19*x+1*y=-6
- 2*x+4*y=-1
- 4*x-20*y=1
-
Identical expressions
- sin^ two (x)+6cos^ two (x)-5sinx*cosx= zero
- sinus of squared (x) plus 6 co sinus of e of squared (x) minus 5 sinus of x multiply by co sinus of e of x equally 0
- sinus of to the power of two (x) plus 6 co sinus of e of to the power of two (x) minus 5 sinus of x multiply by co sinus of e of x equally zero
- sin2(x)+6cos2(x)-5sinx*cosx=0
- sin2x+6cos2x-5sinx*cosx=0
- sin²(x)+6cos²(x)-5sinx*cosx=0
- sin to the power of 2(x)+6cos to the power of 2(x)-5sinx*cosx=0
- sin^2(x)+6cos^2(x)-5sinxcosx=0
- sin2(x)+6cos2(x)-5sinxcosx=0
- sin2x+6cos2x-5sinxcosx=0
- sin^2x+6cos^2x-5sinxcosx=0
- sin^2(x)+6cos^2(x)-5sinx*cosx=O
-
Similar expressions
- sin^2(x)+6cos^2(x)+5sinx*cosx=0
- sin^2(x)-6cos^2(x)-5sinx*cosx=0
sin^2(x)+6cos^2(x)-5sinx*cosx=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
2 2 sin (x) + 6*cos (x) - 5*sin(x)*cos(x) = 0
$$\left(\sin^{2}{\left(x \right)} + 6 \cos^{2}{\left(x \right)}\right) - 5 \sin{\left(x \right)} \cos{\left(x \right)} = 0$$
Sum and product of roots
[src]
sum
/ ____\ / ____\ / ___\ / ___\
|1 \/ 10 | |1 \/ 10 | |1 \/ 5 | |1 \/ 5 |
- 2*atan|- - ------| - 2*atan|- + ------| - 2*atan|- - -----| - 2*atan|- + -----|
\3 3 / \3 3 / \2 2 / \2 2 /
$$- 2 \operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{5}}{2} \right)} + \left(\left(- 2 \operatorname{atan}{\left(\frac{1}{3} + \frac{\sqrt{10}}{3} \right)} - 2 \operatorname{atan}{\left(\frac{1}{3} - \frac{\sqrt{10}}{3} \right)}\right) - 2 \operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{5}}{2} \right)}\right)$$
=
/ ___\ / ___\ / ____\ / ____\
|1 \/ 5 | |1 \/ 5 | |1 \/ 10 | |1 \/ 10 |
- 2*atan|- + -----| - 2*atan|- - -----| - 2*atan|- - ------| - 2*atan|- + ------|
\2 2 / \2 2 / \3 3 / \3 3 /
$$- 2 \operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{5}}{2} \right)} - 2 \operatorname{atan}{\left(\frac{1}{3} + \frac{\sqrt{10}}{3} \right)} - 2 \operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{5}}{2} \right)} - 2 \operatorname{atan}{\left(\frac{1}{3} - \frac{\sqrt{10}}{3} \right)}$$
product
/ ____\ / ____\ / ___\ / ___\
|1 \/ 10 | |1 \/ 10 | |1 \/ 5 | |1 \/ 5 |
-2*atan|- - ------|*-2*atan|- + ------|*-2*atan|- - -----|*-2*atan|- + -----|
\3 3 / \3 3 / \2 2 / \2 2 /
$$- 2 \operatorname{atan}{\left(\frac{1}{3} - \frac{\sqrt{10}}{3} \right)} \left(- 2 \operatorname{atan}{\left(\frac{1}{3} + \frac{\sqrt{10}}{3} \right)}\right) \left(- 2 \operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{5}}{2} \right)}\right) \left(- 2 \operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{5}}{2} \right)}\right)$$
=
/ ___\ / ___\ / ____\ / ____\
|1 \/ 5 | |1 \/ 5 | |1 \/ 10 | |1 \/ 10 |
16*atan|- + -----|*atan|- - -----|*atan|- - ------|*atan|- + ------|
\2 2 / \2 2 / \3 3 / \3 3 /
$$16 \operatorname{atan}{\left(\frac{1}{3} - \frac{\sqrt{10}}{3} \right)} \operatorname{atan}{\left(\frac{1}{3} + \frac{\sqrt{10}}{3} \right)} \operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{5}}{2} \right)} \operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{5}}{2} \right)}$$
16*atan(1/2 + sqrt(5)/2)*atan(1/2 - sqrt(5)/2)*atan(1/3 - sqrt(10)/3)*atan(1/3 + sqrt(10)/3)
Rapid solution
[src]
/ ____\
|1 \/ 10 |
x1 = -2*atan|- - ------|
\3 3 /
$$x_{1} = - 2 \operatorname{atan}{\left(\frac{1}{3} - \frac{\sqrt{10}}{3} \right)}$$
/ ____\
|1 \/ 10 |
x2 = -2*atan|- + ------|
\3 3 /
$$x_{2} = - 2 \operatorname{atan}{\left(\frac{1}{3} + \frac{\sqrt{10}}{3} \right)}$$
/ ___\
|1 \/ 5 |
x3 = -2*atan|- - -----|
\2 2 /
$$x_{3} = - 2 \operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{5}}{2} \right)}$$
/ ___\
|1 \/ 5 |
x4 = -2*atan|- + -----|
\2 2 /
$$x_{4} = - 2 \operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{5}}{2} \right)}$$
x4 = -2*atan(1/2 + sqrt(5)/2)
Numerical answer
[src]
x1 = -5.1760365893855
x2 = -20.8839998573345
x3 = 67.0805944431797
x4 = -875.397201633759
x5 = 20.098601693937
x6 = 7.53223107957784
x7 = -33.4503704716936
x8 = -36.4500660706793
x9 = 92.2133356718981
x10 = 89.2136400729125
x11 = 23.0982972929226
x12 = 98.4965209790777
x13 = -58.4412146458078
x14 = 32.523075253692
x15 = 13.6735193321533
x16 = -108.848594157849
x17 = -17.7424072037447
x18 = -55.4415190468222
x19 = 45.2313429226554
x20 = -71.1494823147711
x21 = -86.715548528116
x22 = 13.8154163867574
x23 = -39.7335557788732
x24 = -8.31762924297529
x25 = 79.7888621121431
x26 = -24767.0674351295
x27 = 95.496825380092
x28 = -49.1583337396426
x29 = 4.24874137138388
x30 = -42.875148432463
x31 = 42.0897502690656
x32 = -52.1580293386282
x33 = 29.5233796547064
x34 = 1.10714871779409
x35 = 16.8151119857431
x36 = -14.4589174955507
x37 = -11.4592218965651
x38 = -61.7247043540018
x39 = -20.7421028027303
x40 = 82.7885577111287
x41 = 57.7977135370145
x42 = -24.0255925109243
x43 = 10.5319266785635
x44 = 73.5056768049635
x45 = 64.0808988441941
x46 = -74.1491779137568
x47 = -86.8574455827201
x48 = -42.7332513778588
x49 = -99.4238161970793
x50 = -89.9990382363099
x51 = 23.2401943475268
x52 = -64.8662970075916
x53 = -27.167185164514
x54 = 60.7974091360002
x55 = -68.0078896611814
x56 = -80.4323632209364
x57 = -8.17573218837112
x58 = -83.7158529291303
x59 = 1.24904577239825
x60 = -8880.03338592595
x61 = -46.0167410860528
x62 = -162.113772214271
x63 = 89.0717430183083
x64 = 35.806564961886
x65 = 76.5053724039491
x66 = -64.7243999529874
x67 = 54.5142238288206
x68 = 38.8062605608716
x69 = -30.1668807634997
x70 = -96.1403264888853
x71 = 48.231038521641
x72 = 70.2221870967695
x73 = -93.1406308898997
x74 = 51.5145282298349
x75 = -77.4326676219507
x76 = 26.2398899465124
x77 = 67.2224914977839
x78 = 86.0720474193227
x79 = -2.0344439357957
x80 = 45.0894458680512
x80 = 45.0894458680512