Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation (2x-4)(x-11)+28=0
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Equation sin(x)=-1/7
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Equation x^2-5x+9=0
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Equation (y+5,214):6,4=10,02
- Express {x} in terms of y where:
- 8*x+7*y=-13
- 5*x+5*y=20
- 2*x+13*y=19
- 14*x-16*y=14
- Derivative of:
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sin(x)
- Integral of d{x}:
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sin(x)
- Canonical form:
- sin(x)
- Limit of the function:
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-1/7
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Identical expressions
- sin(x)=- one / seven
- sinus of (x) equally minus 1 divide by 7
- sinus of (x) equally minus one divide by seven
- sinx=-1/7
- sin(x)=-1 divide by 7
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Similar expressions
- ✓8+10cosx=2sinx
- (2x+1)/(2x-1)-3(2x-1)/(7(2x+1))+8/(1-4x^2)=0
- 4sin3x+sin5x-2sinxcos2x=0
- (x(x-1))/(7)-(2(x^2+1))/(28)=((x-1)(x+2))/(14)
- (9x-4)/5-(6x-1)/7=5
- sin(x)=+1/7
- sinx=-1/7
sin(x)=-1/7 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$\sin{\left(x \right)} = - \frac{1}{7}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$x = 2 \pi n + \operatorname{asin}{\left(- \frac{1}{7} \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(- \frac{1}{7} \right)} + \pi$$
Or
$$x = 2 \pi n - \operatorname{asin}{\left(\frac{1}{7} \right)}$$
$$x = 2 \pi n + \operatorname{asin}{\left(\frac{1}{7} \right)} + \pi$$
, where n - is a integer
$$\sin{\left(x \right)} = - \frac{1}{7}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$x = 2 \pi n + \operatorname{asin}{\left(- \frac{1}{7} \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(- \frac{1}{7} \right)} + \pi$$
Or
$$x = 2 \pi n - \operatorname{asin}{\left(\frac{1}{7} \right)}$$
$$x = 2 \pi n + \operatorname{asin}{\left(\frac{1}{7} \right)} + \pi$$
, where n - is a integer
Rapid solution
[src]
x1 = pi + asin(1/7)
$$x_{1} = \operatorname{asin}{\left(\frac{1}{7} \right)} + \pi$$
x2 = -asin(1/7)
$$x_{2} = - \operatorname{asin}{\left(\frac{1}{7} \right)}$$
x2 = -asin(1/7)
Sum and product of roots
[src]
sum
pi + asin(1/7) - asin(1/7)
$$- \operatorname{asin}{\left(\frac{1}{7} \right)} + \left(\operatorname{asin}{\left(\frac{1}{7} \right)} + \pi\right)$$
=
pi
$$\pi$$
product
(pi + asin(1/7))*(-asin(1/7))
$$\left(\operatorname{asin}{\left(\frac{1}{7} \right)} + \pi\right) \left(- \operatorname{asin}{\left(\frac{1}{7} \right)}\right)$$
=
-(pi + asin(1/7))*asin(1/7)
$$- \left(\operatorname{asin}{\left(\frac{1}{7} \right)} + \pi\right) \operatorname{asin}{\left(\frac{1}{7} \right)}$$
-(pi + asin(1/7))*asin(1/7)
Numerical answer
[src]
x1 = -103.529209999558
x2 = 84.9663492158298
x3 = 97.532719830189
x4 = -94.3911271765992
x5 = 40.9840520655727
x6 = -56.6920153335216
x7 = 94.1044320387884
x8 = -37.8424594119829
x9 = -34.4141716205824
x10 = -9.28143039186401
x11 = -53.2637275421211
x12 = 12.4230230454538
x13 = 62.6885055028905
x14 = -44.1256447191625
x15 = -97.2460246923782
x16 = -90.9628393851986
x17 = 47.2672373727523
x18 = 68.9716908100701
x19 = 9.56812552967475
x20 = -25.2760887976237
x21 = 24.989393659813
x22 = 298.594649659936
x23 = 75.2548761172497
x24 = -15.5646156990436
x25 = -12.7097181832645
x26 = 6.13983773827422
x27 = -18.9929034904441
x28 = 50.1221348885313
x29 = 66.116793294291
x30 = 87.8212467316089
x31 = 3.28494022249516
x32 = 31.2725789669926
x33 = 81.5380614244293
x34 = -59.5469128493007
x35 = -81.82475656224
x36 = -69.2583859478808
x37 = -40.6973569277619
x38 = -50.4088300263421
x39 = -46.9805422349415
x40 = -84.6796540780191
x41 = 37.5557642741722
x42 = -62.9752006407012
x43 = 91.2495345230094
x44 = -65.8300981564803
x45 = 34.7008667583931
x46 = -31.5592741048033
x47 = -2.99824508468443
x48 = -88.1079418694196
x49 = 22.1344961440339
x50 = 28.4176814512135
x51 = 100.387617345968
x52 = -28.1309863134028
x53 = -0.143347568905365
x54 = -75.5415712550604
x55 = 78.6831639086502
x56 = 72.3999786014706
x57 = -100.674312483779
x58 = 15.8513108368543
x59 = 263.750435332637
x60 = 56.4053201957109
x61 = 43.8389495813517
x62 = -21.8478010062232
x63 = 18.7062083526334
x64 = 53.5504226799318
x65 = -72.1132834636599
x66 = 59.8336079871114
x67 = -6.42653287608495
x68 = -78.3964687708395
x68 = -78.3964687708395
The graph