Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation x^2=49
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Equation cos(pi*(x-1)/3)=1/2
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Equation 3*x^2-3=0
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Equation 5(7x+3)-12=4(9x-6)
- Express {x} in terms of y where:
- 18*x-14*y=-12
- 4*x-18*y=-14
- -14*x-1*y=3
- 10*x-18*y=6
- Derivative of:
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sinx-cosx
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1/2
- Integral of d{x}:
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sinx-cosx
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1/2
- Canonical form:
- sinx-cosx
- Sum of series:
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1/2
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Identical expressions
- sinx-cosx= one / two
- sinus of x minus co sinus of e of x equally 1 divide by 2
- sinus of x minus co sinus of e of x equally one divide by two
- sinx-cosx=1 divide by 2
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Similar expressions
- 2*sin(x)-cos(x)=sqrt(3)*sin(x)
- sin(3x)=sqrt(2)(sin(x)-cos(x))
- sinx+cosx=1/2
- sin(x)-cos(x)=1
sinx-cosx=1/2 equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
sin(x) - cos(x) = 1/2
$$\sin{\left(x \right)} - \cos{\left(x \right)} = \frac{1}{2}$$
Rapid solution
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/ ___\ x1 = -2*atan\2 - \/ 7 /
$$x_{1} = - 2 \operatorname{atan}{\left(2 - \sqrt{7} \right)}$$
/ ___\ x2 = -2*atan\2 + \/ 7 /
$$x_{2} = - 2 \operatorname{atan}{\left(2 + \sqrt{7} \right)}$$
x2 = -2*atan(2 + sqrt(7))
Sum and product of roots
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sum
/ ___\ / ___\ - 2*atan\2 - \/ 7 / - 2*atan\2 + \/ 7 /
$$- 2 \operatorname{atan}{\left(2 + \sqrt{7} \right)} - 2 \operatorname{atan}{\left(2 - \sqrt{7} \right)}$$
=
/ ___\ / ___\ - 2*atan\2 + \/ 7 / - 2*atan\2 - \/ 7 /
$$- 2 \operatorname{atan}{\left(2 + \sqrt{7} \right)} - 2 \operatorname{atan}{\left(2 - \sqrt{7} \right)}$$
product
/ ___\ / ___\ -2*atan\2 - \/ 7 /*-2*atan\2 + \/ 7 /
$$- 2 \operatorname{atan}{\left(2 - \sqrt{7} \right)} \left(- 2 \operatorname{atan}{\left(2 + \sqrt{7} \right)}\right)$$
=
/ ___\ / ___\ 4*atan\2 + \/ 7 /*atan\2 - \/ 7 /
$$4 \operatorname{atan}{\left(2 - \sqrt{7} \right)} \operatorname{atan}{\left(2 + \sqrt{7} \right)}$$
4*atan(2 + sqrt(7))*atan(2 - sqrt(7))
Numerical answer
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x1 = 53.8311061505172
x2 = -99.3841996275692
x3 = -74.2514583988509
x4 = 1.14676528730416
x5 = -59.2662293787153
x6 = 7.42995059448374
x7 = 72.680662072056
x8 = -42.8355318629529
x9 = 85.2470326864152
x10 = 47.5479208433376
x11 = -90.6821559146133
x12 = 63.9786183591
x13 = 9.84880900026012
x14 = 38.8458771303817
x15 = 45.1290624375613
x16 = 34.9815502289785
x17 = -30.2691612485938
x18 = 57.6954330519204
x19 = -23.9859759414142
x20 = -21.5671175356378
x21 = 16.1319943074397
x22 = 361.707186202317
x23 = 76.5449889734592
x24 = -67.9682730916713
x25 = 19.9963212088429
x26 = 28.6983649217989
x27 = -2.71756161409905
x28 = 41.264735536158
x29 = 660.881222541161
x30 = 95.3945448949979
x31 = 91.5302179935947
x32 = -93.1010143203896
x33 = -5.13642001987543
x34 = 26.2795065160225
x35 = -52.9830440715357
x36 = 97.8134033007743
x37 = -96.9653412217929
x38 = -84.3989706074337
x39 = -71.8325999930745
x40 = -17.7027906342346
x41 = 78.9638473792356
x42 = -40.4166734571766
x43 = -61.6850877844917
x44 = -49.1187171701325
x45 = -9.00074692127864
x46 = -34.133488149997
x47 = -46.6998587643562
x48 = -65.5494146858949
x49 = 32.5626918232021
x50 = 51.4122477447408
x51 = -27.8503028428174
x52 = -15.2839322284582
x53 = 104.096588607954
x54 = 82.8281742806388
x55 = 13.7131359016633
x56 = -86.8178290132101
x57 = -11.419605327055
x58 = 66.3974767648764
x59 = 70.2618036662796
x60 = -36.5523465557734
x61 = -80.5346437060305
x62 = 22.4151796146193
x63 = 60.1142914576968
x64 = -55.4019024773121
x65 = -78.1157853002541
x66 = 89.1113595878184
x67 = 3.56562369308053
x67 = 3.56562369308053