Mister Exam
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How to use it?
- Equation:
-
Equation tg(x)=-1/2
-
Equation 8x-4=9x-2(2x-7)
-
Equation cos(x/8+pi/4)=1
-
Equation ctg(x/2)=√3
- Express {x} in terms of y where:
- -12*x+3*y=-9
- 14*x-16*y=14
- -10*x+18*y=6
- 9*x-18*y=6
-
Identical expressions
- cos(x/ eight +pi/ four)= one
- co sinus of e of (x divide by 8 plus Pi divide by 4) equally 1
- co sinus of e of (x divide by eight plus Pi divide by four) equally one
- cosx/8+pi/4=1
- cos(x divide by 8+pi divide by 4)=1
-
Similar expressions
- cos(x/8-pi/4)=1
cos(x/8+pi/4)=1 equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
/x pi\ cos|- + --| = 1 \8 4 /
$$\cos{\left(\frac{x}{8} + \frac{\pi}{4} \right)} = 1$$
Detail solution
Given the equation
$$\cos{\left(\frac{x}{8} + \frac{\pi}{4} \right)} = 1$$
- this is the simplest trigonometric equation
This equation is transformed to
$$\frac{x}{8} + \frac{\pi}{4} = 2 \pi n + \operatorname{acos}{\left(1 \right)}$$
$$\frac{x}{8} + \frac{\pi}{4} = 2 \pi n - \pi + \operatorname{acos}{\left(1 \right)}$$
Or
$$\frac{x}{8} + \frac{\pi}{4} = 2 \pi n$$
$$\frac{x}{8} + \frac{\pi}{4} = 2 \pi n - \pi$$
, where n - is a integer
Move
$$\frac{\pi}{4}$$
to right part of the equation with the opposite sign, in total:
$$\frac{x}{8} = 2 \pi n - \frac{\pi}{4}$$
$$\frac{x}{8} = 2 \pi n - \frac{5 \pi}{4}$$
Divide both parts of the equation by
$$\frac{1}{8}$$
we get the answer:
$$x_{1} = 16 \pi n - 2 \pi$$
$$x_{2} = 16 \pi n - 10 \pi$$
$$\cos{\left(\frac{x}{8} + \frac{\pi}{4} \right)} = 1$$
- this is the simplest trigonometric equation
This equation is transformed to
$$\frac{x}{8} + \frac{\pi}{4} = 2 \pi n + \operatorname{acos}{\left(1 \right)}$$
$$\frac{x}{8} + \frac{\pi}{4} = 2 \pi n - \pi + \operatorname{acos}{\left(1 \right)}$$
Or
$$\frac{x}{8} + \frac{\pi}{4} = 2 \pi n$$
$$\frac{x}{8} + \frac{\pi}{4} = 2 \pi n - \pi$$
, where n - is a integer
Move
$$\frac{\pi}{4}$$
to right part of the equation with the opposite sign, in total:
$$\frac{x}{8} = 2 \pi n - \frac{\pi}{4}$$
$$\frac{x}{8} = 2 \pi n - \frac{5 \pi}{4}$$
Divide both parts of the equation by
$$\frac{1}{8}$$
we get the answer:
$$x_{1} = 16 \pi n - 2 \pi$$
$$x_{2} = 16 \pi n - 10 \pi$$
Sum and product of roots
[src]
sum
-2*pi + 14*pi
$$\left(- 2 \pi\right) + \left(14 \pi\right)$$
=
12*pi
$$12 \pi$$
product
-2*pi * 14*pi
$$\left(- 2 \pi\right) * \left(14 \pi\right)$$
=
2 -28*pi
$$- 28 \pi^{2}$$
Numerical answer
[src]
x1 = -106.814146259303
x2 = 94.2477796093523
x3 = 43.9822954389537
x4 = -56.54867580794
x5 = -56.5486717708719
x6 = -56.5486647535881
x7 = -6.28318602316776
x8 = -106.814146347399
x9 = -6.28318735173461
x10 = -56.5486708047995
x11 = 94.2477755202581
x12 = -6.28318131104164
x13 = -6.28318143493258
x14 = -6.28318512418657
x15 = 94.2477769906178
x16 = -56.5486656889023
x17 = -56.5486638231441
x18 = 43.9822990068294
x19 = 43.9823005247175
x20 = 43.9822954991962
x21 = -106.814146097798
x22 = -6.28318181321916
x23 = -56.5486683532657
x24 = 43.9822982995603
x25 = -6.28318119421106
x26 = 43.9822930845907
x27 = 94.2477861819348
x28 = -56.5486638449637
x29 = 43.9823040449486
x30 = 43.9822981362514
x31 = 94.2477804739555
x32 = -56.5486692478789
x33 = -6.28318690506942
x34 = -106.814147291951
x35 = -6.2831833402855
x36 = -6.28318934569098
x37 = -6.28318601724157
x38 = -6.2831937811219
x39 = -56.5486713869336
x40 = -157.079634939341
x41 = 43.9822946326014
x42 = 43.9823012482613
x43 = -56.5486715149823
x44 = -6.28318895482682
x45 = 43.9822963195339
x46 = 94.2477777842769
x47 = -56.548664295998
x48 = -56.5486654842072
x49 = 94.2477813525311
x50 = 94.2477786570642
x51 = -6.28318420227934
x52 = -56.5486701441855
x53 = 94.2477784203741
x54 = -106.814146682021
x55 = -106.814151074373
x56 = -6.28318940114689
x57 = -56.5486718735468
x58 = -6.28318210049443
x59 = 43.982293939466
x60 = -6.28318772342667
x61 = 194.778751454351
x62 = -6.28318256385204
x63 = -56.5486674525757
x64 = -56.5486700775614
x65 = -56.5486636427642
x66 = -56.5486665416948
x67 = -56.5486678307325
x68 = -6.28318899323361
x69 = 43.9822936235391
x70 = -6.28318471346981
x71 = -56.5486649267485
x72 = -56.5486776860704
x73 = -6.28318191311595
x74 = 94.2477763156869
x75 = -106.814159376448
x76 = 94.2477821554189
x77 = 43.982300466748
x78 = 43.9823009709802
x79 = 43.9822930796088
x80 = 43.9822904462094
x81 = 43.9823020765976
x82 = 94.2477758051249
x83 = -106.814147439206
x84 = 43.9822997968378
x85 = 43.9822971694769
x86 = 43.9822934040677
x87 = -307.876085800017
x88 = -6.28318843399251
x89 = 194.778747772782
x90 = 43.9823011900812
x91 = 94.2477755694512
x92 = 94.2477762226776
x92 = 94.2477762226776
The graph