Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation 2sinx=5cosx
-
Equation 5(x+1)(x-3)=4x^2-8x
-
Equation x³-2x²+2x-4=0
- Equation 2log16(2x−5)=2
- Express {x} in terms of y where:
- 9*x+18*y=6
- 15*x-15*y=16
- (x^2+y^2-1)^3+x^2*y^3=0
- -1*x-19*y=-10
- Integral of d{x}:
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2sinx
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5cosx
- Graphing y =:
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2sinx
- Derivative of:
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2sinx
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5cosx
-
Identical expressions
- 2sinx=5cosx
- 2 sinus of x equally 5 co sinus of e of x
-
Similar expressions
- cos9(x)-cos7(x)=√2sin(x)
- (5*cos(x)-3)/(3*tg(x)+4)=0
- 2sin^2(x)-5cos(x)+1=0
2sinx=5cosx equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$2 \sin{\left(x \right)} = 5 \cos{\left(x \right)}$$
transform:
$$\frac{2 \sin{\left(x \right)}}{\cos{\left(x \right)}} = 5$$
or
$$2 \tan{\left(x \right)} = 5$$
- this is the simplest trigonometric equation
Divide both parts of the equation by $2$
The equation is transformed to
$$\tan{\left(x \right)} = - \frac{5}{2}$$
This equation is transformed to
$$x = \pi n + \operatorname{atan}{\left(- \frac{5}{2} \right)}$$
Or
$$x = \pi n - \operatorname{atan}{\left(\frac{5}{2} \right)}$$
, where n - is a integer
$$2 \sin{\left(x \right)} = 5 \cos{\left(x \right)}$$
transform:
$$\frac{2 \sin{\left(x \right)}}{\cos{\left(x \right)}} = 5$$
or
$$2 \tan{\left(x \right)} = 5$$
- this is the simplest trigonometric equation
Divide both parts of the equation by $2$
The equation is transformed to
$$\tan{\left(x \right)} = - \frac{5}{2}$$
This equation is transformed to
$$x = \pi n + \operatorname{atan}{\left(- \frac{5}{2} \right)}$$
Or
$$x = \pi n - \operatorname{atan}{\left(\frac{5}{2} \right)}$$
, where n - is a integer
Sum and product of roots
[src]
sum
atan(5/2)
$$\left(\operatorname{atan}{\left(\frac{5}{2} \right)}\right)$$
=
atan(5/2)
$$\operatorname{atan}{\left(\frac{5}{2} \right)}$$
product
atan(5/2)
$$\left(\operatorname{atan}{\left(\frac{5}{2} \right)}\right)$$
=
atan(5/2)
$$\operatorname{atan}{\left(\frac{5}{2} \right)}$$
Numerical answer
[src]
x1 = -20.800858625446
x2 = -83.6327116972419
x3 = 95.4380695573763
x4 = 92.2964769037865
x5 = 20.0398458712213
x6 = -55.3583778149337
x7 = 5665.48184437208
x8 = -74.2079337364725
x9 = 51.4557724071192
x10 = -39.6504145469848
x11 = 57.7389577142988
x12 = 79.7301062894274
x13 = 16.8982532176315
x14 = 64.0221430214784
x15 = -36.508821893395
x16 = 10.6150679104519
x17 = 67.1637356750682
x18 = -501.464534624684
x19 = 60.8805503678886
x20 = 29.4646238319907
x21 = 1.19028994968253
x22 = 54.597365060709
x23 = 23.1814385248111
x24 = -33.3672292398052
x25 = 32.6062164855805
x26 = -27.0840439326256
x27 = -58.4999704685235
x28 = 13.7566605640417
x29 = 4.33188260327232
x30 = 89.1548842501967
x31 = -52.216785161344
x32 = -96.1990823116011
x33 = -14.5176733182664
x34 = -30.2256365862154
x35 = 26.3230311784009
x36 = -209.296417840834
x37 = -102.482267618781
x38 = -67.9247484292929
x39 = -11.3760806646766
x40 = -71.0663410828827
x41 = 86.0132915966069
x42 = 73.4469209822478
x43 = 434.730076145074
x44 = 38.88940179276
x45 = -80.4911190436521
x46 = -89.9158970044215
x47 = 5379.59691289541
x48 = -86.7743043508317
x49 = 76.5885136358376
x50 = 35.7478091391703
x51 = -5.09289535749705
x52 = -99.3406749651909
x53 = -61.6415631221133
x54 = 481.853965948921
x55 = -17.6592659718562
x56 = 42.0309944463498
x57 = -8.23448801108685
x58 = -77.3495263900623
x59 = -42.7920072005746
x60 = 7.47347525686212
x61 = 70.305328328658
x62 = -93.0574896580113
x63 = 48.3141797535294
x64 = -45.9335998541644
x65 = -64.7831557757031
x66 = 98.5796622109661
x67 = 45.1725870999396
x68 = 82.8716989430172
x69 = -23.9424512790358
x70 = -1.95130270390726
x71 = -49.0751925077542
x71 = -49.0751925077542
The graph