Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation cos(x)=1/3
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Equation sin5x-√3cos5x=0
- Equation (√x-6)(2x^2-x-15)=0
- Equation Cos3xcos5x-sin3xsin5x=0
- Express {x} in terms of y where:
- -11*x+4*y=-8
- -14*x+1*y=3
- 14*x+16*y=14
- 16*x+7*y=8
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Identical expressions
- sin5x-√3cos5x= zero
- sinus of 5x minus √3 co sinus of e of 5x equally 0
- sinus of 5x minus √3 co sinus of e of 5x equally zero
- sin5x-√3cos5x=O
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Similar expressions
- sin5x+√3cos5x=0
sin5x-√3cos5x=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
____________ sin(5*x) - \/ 3*cos(5*x) = 0
$$- \sqrt{3 \cos{\left(5 x \right)}} + \sin{\left(5 x \right)} = 0$$
Rapid solution
[src]
/ _____________\
| ___ / ____ |
|\/ 3 *\/ -2 + \/ 13 |
2*atan|----------------------|
\ 3 /
x1 = ------------------------------
5
$$x_{1} = \frac{2 \operatorname{atan}{\left(\frac{\sqrt{3} \sqrt{-2 + \sqrt{13}}}{3} \right)}}{5}$$
Sum and product of roots
[src]
sum
/ _____________\
| ___ / ____ |
|\/ 3 *\/ -2 + \/ 13 |
2*atan|----------------------|
\ 3 /
0 + ------------------------------
5
$$0 + \frac{2 \operatorname{atan}{\left(\frac{\sqrt{3} \sqrt{-2 + \sqrt{13}}}{3} \right)}}{5}$$
=
/ _____________\
| ___ / ____ |
|\/ 3 *\/ -2 + \/ 13 |
2*atan|----------------------|
\ 3 /
------------------------------
5
$$\frac{2 \operatorname{atan}{\left(\frac{\sqrt{3} \sqrt{-2 + \sqrt{13}}}{3} \right)}}{5}$$
product
/ _____________\
| ___ / ____ |
|\/ 3 *\/ -2 + \/ 13 |
2*atan|----------------------|
\ 3 /
1*------------------------------
5
$$1 \cdot \frac{2 \operatorname{atan}{\left(\frac{\sqrt{3} \sqrt{-2 + \sqrt{13}}}{3} \right)}}{5}$$
=
/ _____________\
| ___ / ____ |
|\/ 3 *\/ -2 + \/ 13 |
2*atan|----------------------|
\ 3 /
------------------------------
5
$$\frac{2 \operatorname{atan}{\left(\frac{\sqrt{3} \sqrt{-2 + \sqrt{13}}}{3} \right)}}{5}$$
2*atan(sqrt(3)*sqrt(-2 + sqrt(13))/3)/5
Numerical answer
[src]
x1 = 10.3057350269402
x2 = -43.7296586148043
x3 = 54.2880321771973
x4 = -60.0659404134712
x5 = -93.995141072241
x6 = -16.0836432632141
x7 = 98.2703293274544
x8 = 37.9517503785304
x9 = 84.4473216516593
x10 = -19.8535544475218
x11 = 68.1110398529924
x12 = 74.394225160172
x13 = 58.057943361505
x14 = 48.0048468700177
x15 = 4.02254971976059
x16 = -67.6057627820867
x17 = 88.2172328359671
x18 = -13.5703691403423
x19 = -29.9066509390092
x20 = -63.8358515977789
x21 = -73.8889480892663
x22 = -77.658859273574
x23 = 81.9340475287875
x24 = -33.6765621233169
x25 = -87.7119557650614
x26 = -83.9420445807536
x27 = 64.3411286686846
x28 = 14.0756462112479
x29 = -57.5526662905994
x30 = 44.2349356857099
x31 = -23.6234656318296
x32 = 35.8141562509236 + 0.372832308831576*i
x33 = -9.8004579560345
x34 = -39.9597474304965
x35 = 34.1818391942226
x36 = -6.03054677172675
x37 = -97.7650522565487
x38 = 0.252638535452837
x39 = -50.0128439219839
x40 = 20.3588315184275
x41 = -53.7827551062916
x42 = 30.4119280099149
x43 = 78.1641363444797
x44 = 24.1287427027353
x45 = -38.7031103690606
x46 = 91.9871440202748
x46 = 91.9871440202748
The graph