Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation x^2=7
-
Equation sin(x)=1/8
- Equation xy
-
Equation 600-(x-37)=417
- Express {x} in terms of y where:
- 4*x-16*y=6
- sqrt(x^2+y^2+4x-6y-12)+(x^2+10x-27)=8-|y-9|+|y-3|
- 10*x-1*y=10
- 15*x-17*y=19
- Derivative of:
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sin(x)
- 1/8
- Integral of d{x}:
-
sin(x)
- 1/8
- Canonical form:
- sin(x)
- Sum of series:
-
1/8
-
Identical expressions
- sin(x)= one / eight
- sinus of (x) equally 1 divide by 8
- sinus of (x) equally one divide by eight
- sinx=1/8
- sin(x)=1 divide by 8
-
Similar expressions
- 2=log2(1/(8/n))
- (2sin((3pi)/2+2x)^2+sin(4x))/log3(2^(1/2)*sinx)=0
- 4sin²x-5sinxcosx+cos²x=0
- sinx+cosx=0
- sinx=1/8
sin(x)=1/8 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$\sin{\left(x \right)} = \frac{1}{8}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$x = 2 \pi n + \operatorname{asin}{\left(\frac{1}{8} \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(\frac{1}{8} \right)} + \pi$$
Or
$$x = 2 \pi n + \operatorname{asin}{\left(\frac{1}{8} \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(\frac{1}{8} \right)} + \pi$$
, where n - is a integer
$$\sin{\left(x \right)} = \frac{1}{8}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$x = 2 \pi n + \operatorname{asin}{\left(\frac{1}{8} \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(\frac{1}{8} \right)} + \pi$$
Or
$$x = 2 \pi n + \operatorname{asin}{\left(\frac{1}{8} \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(\frac{1}{8} \right)} + \pi$$
, where n - is a integer
Rapid solution
[src]
x1 = pi - asin(1/8)
$$x_{1} = \pi - \operatorname{asin}{\left(\frac{1}{8} \right)}$$
x2 = asin(1/8)
$$x_{2} = \operatorname{asin}{\left(\frac{1}{8} \right)}$$
Sum and product of roots
[src]
sum
0 + pi - asin(1/8) + asin(1/8)
$$\operatorname{asin}{\left(\frac{1}{8} \right)} + \left(0 + \left(\pi - \operatorname{asin}{\left(\frac{1}{8} \right)}\right)\right)$$
=
pi
$$\pi$$
product
1*(pi - asin(1/8))*asin(1/8)
$$1 \left(\pi - \operatorname{asin}{\left(\frac{1}{8} \right)}\right) \operatorname{asin}{\left(\frac{1}{8} \right)}$$
=
(pi - asin(1/8))*asin(1/8)
$$\left(\pi - \operatorname{asin}{\left(\frac{1}{8} \right)}\right) \operatorname{asin}{\left(\frac{1}{8} \right)}$$
(pi - asin(1/8))*asin(1/8)
Numerical answer
[src]
x1 = -75.272895854987
x2 = -40.9660323278354
x3 = 12.6916984455272
x4 = 84.6976738157563
x5 = -28.3996617134762
x6 = 6.40851313834765
x7 = 44.1076249814252
x8 = 15.5826354367809
x9 = -84.9483294780925
x10 = -91.2315147852721
x11 = 97.2640444301155
x12 = -72.3819588637333
x13 = -50.1401546262686
x14 = -87.8392664693461
x15 = 0.125327831168065
x16 = -94.1224517765257
x17 = -25.0074133975503
x18 = -22.1164764062966
x19 = -3.26692048475786
x20 = -43.856969319089
x21 = 69.2403662101435
x22 = 81.8067368245027
x23 = -56.4233399334482
x24 = -12.4410427831911
x25 = 3.01626482242173
x26 = -34.6828470206558
x27 = 62.9571809029639
x28 = 34.4321913583197
x29 = -53.5324029421946
x30 = -97.5147000924517
x31 = 144.638589896299
x32 = 103.547229737295
x33 = -59.8155882493741
x34 = 50.3908102886048
x35 = 90.9808591229359
x36 = 21.8658207439605
x37 = -62.7065252406278
x38 = -47.249217635015
x39 = -18.7242280903707
x40 = -147.780182549888
x41 = 18.9748837527068
x42 = 100.656292746041
x43 = 72.1313032013972
x44 = 9.29945012960131
x45 = 28.1490060511401
x46 = 65.8481178942176
x47 = -78.6651441709129
x48 = 75.5235515173231
x49 = -9.55010579193745
x50 = 4181.33449409685
x51 = -37.5737840119095
x52 = 56.6739955957843
x53 = -81.5560811621666
x54 = -68.9897105478074
x55 = 59.564932587038
x56 = 78.4144885085768
x57 = 53.2817472798584
x58 = -6.15785747601152
x59 = 40.7153766654992
x60 = -15.833291099117
x61 = 31.541254367066
x62 = 88.0899221316823
x63 = -31.2905987047299
x64 = -66.0987735565537
x65 = 94.3731074388619
x66 = 37.8244396742456
x67 = -100.405637083705
x68 = 46.9985619726788
x69 = 25.2580690598864
x69 = 25.2580690598864
The graph