Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation sin(x)=pi/2
- Equation x^2-49=0
-
Equation 3*sin(x)=0
- Express {x} in terms of y where:
- 18*x+19*y=7
- 1*x+6*y=6
- -16*x-12*y=12
- -17*x-12*y=-9
- Derivative of:
- cos(x+pi/6)
-
Identical expressions
- cos(x+pi/ six)=sqrt(one)
- co sinus of e of (x plus Pi divide by 6) equally square root of (1)
- co sinus of e of (x plus Pi divide by six) equally square root of (one)
- cos(x+pi/6)=√(1)
- cosx+pi/6=sqrt1
- cos(x+pi divide by 6)=sqrt(1)
-
Similar expressions
- sqrt(14+5*x)=x
- sqrt((10+x)^2+20x)-x=13,66
- (2sin(x)^2-sin(2x)-2cos(2x))/(sqrt1-x^2)=0
- cos(x-pi/6)=sqrt(1)
- sqrt(2x-1)=sqrt(1-2x)
- sqrt(10x+11)=-x
- cos(x+(pi/6))=sqrt(2)/2
cos(x+pi/6)=sqrt(1) equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
/ pi\ ___ cos|x + --| = \/ 1 \ 6 /
$$\cos{\left(x + \frac{\pi}{6} \right)} = \sqrt{1}$$
Detail solution
Given the equation
$$\cos{\left(x + \frac{\pi}{6} \right)} = \sqrt{1}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$x + \frac{\pi}{6} = \pi n + \operatorname{acos}{\left(1 \right)}$$
$$x + \frac{\pi}{6} = \pi n - \pi + \operatorname{acos}{\left(1 \right)}$$
Or
$$x + \frac{\pi}{6} = \pi n$$
$$x + \frac{\pi}{6} = \pi n - \pi$$
, where n - is a integer
Move
$$\frac{\pi}{6}$$
to right part of the equation
with the opposite sign, in total:
$$x = \pi n - \frac{\pi}{6}$$
$$x = \pi n - \frac{7 \pi}{6}$$
$$\cos{\left(x + \frac{\pi}{6} \right)} = \sqrt{1}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$x + \frac{\pi}{6} = \pi n + \operatorname{acos}{\left(1 \right)}$$
$$x + \frac{\pi}{6} = \pi n - \pi + \operatorname{acos}{\left(1 \right)}$$
Or
$$x + \frac{\pi}{6} = \pi n$$
$$x + \frac{\pi}{6} = \pi n - \pi$$
, where n - is a integer
Move
$$\frac{\pi}{6}$$
to right part of the equation
with the opposite sign, in total:
$$x = \pi n - \frac{\pi}{6}$$
$$x = \pi n - \frac{7 \pi}{6}$$
Rapid solution
[src]
-pi
x1 = ----
6
$$x_{1} = - \frac{\pi}{6}$$
11*pi
x2 = -----
6
$$x_{2} = \frac{11 \pi}{6}$$
x2 = 11*pi/6
Sum and product of roots
[src]
sum
pi 11*pi - -- + ----- 6 6
$$- \frac{\pi}{6} + \frac{11 \pi}{6}$$
=
5*pi ---- 3
$$\frac{5 \pi}{3}$$
product
-pi 11*pi ----*----- 6 6
$$- \frac{\pi}{6} \frac{11 \pi}{6}$$
=
2 -11*pi ------- 36
$$- \frac{11 \pi^{2}}{36}$$
-11*pi^2/36
Numerical answer
[src]
x1 = 49.7418835245054
x2 = -69.6386366485818
x3 = 56.0250693524419
x4 = 49.7418831724391
x5 = -50.7890816527148
x6 = -31.9395249202358
x7 = 81.1578093180369
x8 = 87.4409958250878
x9 = -75.9218229143423
x10 = -6.80678449725847
x11 = -88.4881942807791
x12 = 68.5914401276649
x13 = -63.3554513363679
x14 = 43.4586986677198
x15 = 24.6091430772094
x16 = 49.7418838493326
x17 = 24.6091422617441
x18 = -0.523598489731523
x19 = -38.2227111279653
x20 = 30.8923274298613
x21 = 5.75958643339931
x22 = -94.7713788080582
x23 = -75.9218220581853
x24 = 56.0250690081558
x25 = 56.0250689522333
x26 = -82.2050077643523
x27 = 93.7241806097162
x28 = -94.7713780045959
x29 = 12.0427717615073
x30 = -25.65633950106
x31 = -19.373154896527
x32 = 12.0427722166701
x33 = 30.8923274495049
x34 = 5.75958669034246
x35 = 18.3259568926578
x36 = 68.5914401180933
x37 = -19.3731539653969
x38 = 68.5914394200902
x39 = 30.8923282331952
x40 = 62.3082540196632
x41 = -264.417382419922
x42 = 62.308254257502
x43 = 100.007366129962
x44 = -88.4881935647341
x45 = 37.1755126583087
x46 = -44.5058964115732
x47 = 74.8746253871791
x48 = 93.7241810081872
x49 = -38.2227104687978
x50 = -69.638637223832
x51 = 5.75958602210796
x52 = -82.2050076281063
x53 = 43.4586978952293
x54 = 156.556034516879
x55 = 100.007365661841
x56 = 81.1578098139843
x57 = 12.0427713725902
x58 = -19.3731541846809
x59 = -63.3554520547243
x60 = -50.7890808483935
x61 = -25.6563402322524
x62 = 37.1755134637125
x63 = -6.80678369229017
x64 = 18.3259576460966
x65 = -69.6386373548543
x66 = -31.9395254617805
x67 = 301.069297155331
x68 = -88.4881928048828
x69 = 74.8746246066628
x70 = -57.0722660751833
x71 = -38.2227106630569
x72 = -44.5058956472658
x73 = 24.6091429668081
x74 = -13.0899689209265
x75 = -13.0899697075722
x76 = -57.0722665843695
x77 = -44.5058967203222
x78 = 93.7241803230185
x79 = 5.75958726070503
x80 = -31.939525771185
x81 = -63.3554510011992
x82 = 62.3082547928689
x83 = 87.4409950488631
x84 = -0.523599258250701
x85 = 18.3259570967149
x86 = -13.0899698146708
x87 = -57.0722668645673
x88 = -82.2050082777704
x89 = 56.0250685169442
x90 = -25.6563400637071
x91 = 81.1578106196128
x92 = -101.054563229573
x93 = -75.9218228126903
x93 = -75.9218228126903