Mister Exam
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How to use it?
- Equation:
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Equation 3x-7(3x-4)=5(2x-7)
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Equation x^3
- Equation −2∣x+4∣=3−4x-2
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Equation sin2x-cos2x=-0,5
- Express {x} in terms of y where:
- 10*x-1*y=10
- 15*x-17*y=19
- 9*x-8*y=6
- 15*x+15*y=16
- Derivative of:
- sin2x-cos2x
- -0,5
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Identical expressions
- sin2x-cos2x=- zero , five
- sinus of 2x minus co sinus of e of 2x equally minus 0,5
- sinus of 2x minus co sinus of e of 2x equally minus zero , five
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Similar expressions
- sin2x+cos2x=-0,5
- sin2x-cos2x=+0,5
- -sin^2x-cos^2x-2sinx=0
- sin(2x)-cos(2x)=3/4
- sin^2(x)-cos^2(x)=1
sin2x-cos2x=-0,5 equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
sin(2*x) - cos(2*x) = -1/2
$$\sin{\left(2 x \right)} - \cos{\left(2 x \right)} = - \frac{1}{2}$$
Rapid solution
[src]
/ ___\
|2 \/ 7 |
x1 = -atan|- - -----|
\3 3 /
$$x_{1} = - \operatorname{atan}{\left(- \frac{\sqrt{7}}{3} + \frac{2}{3} \right)}$$
/ ___\
|2 \/ 7 |
x2 = -atan|- + -----|
\3 3 /
$$x_{2} = - \operatorname{atan}{\left(\frac{2}{3} + \frac{\sqrt{7}}{3} \right)}$$
Sum and product of roots
[src]
sum
/ ___\ / ___\
|2 \/ 7 | |2 \/ 7 |
0 - atan|- - -----| - atan|- + -----|
\3 3 / \3 3 /
$$- \operatorname{atan}{\left(\frac{2}{3} + \frac{\sqrt{7}}{3} \right)} - \operatorname{atan}{\left(- \frac{\sqrt{7}}{3} + \frac{2}{3} \right)}$$
=
/ ___\ / ___\
|2 \/ 7 | |2 \/ 7 |
- atan|- - -----| - atan|- + -----|
\3 3 / \3 3 /
$$- \operatorname{atan}{\left(\frac{2}{3} + \frac{\sqrt{7}}{3} \right)} - \operatorname{atan}{\left(- \frac{\sqrt{7}}{3} + \frac{2}{3} \right)}$$
product
/ ___\ / ___\
|2 \/ 7 | |2 \/ 7 |
1*-atan|- - -----|*-atan|- + -----|
\3 3 / \3 3 /
$$1 \left(- \operatorname{atan}{\left(- \frac{\sqrt{7}}{3} + \frac{2}{3} \right)}\right) \left(- \operatorname{atan}{\left(\frac{2}{3} + \frac{\sqrt{7}}{3} \right)}\right)$$
=
/ ___\ / ___\
|2 \/ 7 | |2 \/ 7 |
atan|- - -----|*atan|- + -----|
\3 3 / \3 3 /
$$\operatorname{atan}{\left(- \frac{\sqrt{7}}{3} + \frac{2}{3} \right)} \operatorname{atan}{\left(\frac{2}{3} + \frac{\sqrt{7}}{3} \right)}$$
atan(2/3 - sqrt(7)/3)*atan(2/3 + sqrt(7)/3)
Numerical answer
[src]
x1 = -51.2628961405795
x2 = -78.3278008199995
x3 = 28.4863494020535
x4 = -43.7702816305117
x5 = 94.4597951274392
x6 = 14.7105495848061
x7 = 17.8521422383959
x8 = 8.42736427762656
x9 = 58.6928467350633
x10 = 15.9199787876943
x11 = -48.1213034869897
x12 = 61.834439388653
x13 = 30.4185128527551
x14 = -94.0357640879484
x15 = 68.1176246958326
x16 = 50.4774979771821
x17 = 97.601387781029
x18 = 22.2031640948739
x19 = -62.6198375520505
x20 = 74.4008100030122
x21 = -12.3543550946138
x22 = 37.9111273628229
x23 = 83.8255879637816
x24 = -100.318949395128
x25 = -63.8292667549387
x26 = -15.4959477482036
x27 = 31.6279420556433
x28 = -87.7525787807688
x29 = 36.7016981599347
x30 = -85.8204153300672
x31 = 53.6190906307719
x32 = -56.3366522448709
x33 = -72.0446155128199
x34 = 75.6102392059004
x35 = -73.2540447157081
x36 = 80.6839953101918
x37 = -34.3455036697424
x38 = 72.4686465523106
x39 = -59.4782448984607
x40 = -76.3956373692979
x41 = -37.4870963233321
x42 = -13.563784297502
x43 = 24.1353275455755
x44 = 88.1766098202596
x45 = -21.7791330553832
x46 = -79.5372300228877
x47 = 137.232663074808
x48 = 0.21201551974537
x49 = 9.63679348051475
x50 = -40.6286889769219
x51 = -57.5460814477591
x52 = 66.185461245131
x53 = 90.1087732709612
x54 = -29.271747565451
x55 = -98.3867859444264
x56 = 52.4096614278837
x57 = -6.07116978743422
x58 = 59.9022759379514
x59 = -81.4693934735892
x60 = -65.7614302056403
x61 = 91.3182024738494
x62 = -95.2451932908366
x63 = -50.0534669376913
x64 = -19.8469696046816
x65 = -35.5549328726305
x66 = -1000.0238775247
x67 = 39.8432908135245
x68 = -321.439864349302
x69 = -7.2805989903224
x70 = 44.1943126700025
x71 = 6.49520082692496
x72 = -70.1124520621183
x73 = -84.610986127179
x74 = -4.13900633673261
x75 = -28.0623183625628
x76 = 96.3919585781408
x77 = -41.8381181798101
x78 = -92.1036006372468
x79 = 108.9583291925
x80 = 46.1264761207041
x81 = -26.1301549118612
x82 = 81.89342451308
x83 = 2.14417897044697
x83 = 2.14417897044697
The graph