Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation x^2-7*x+10=0
-
Equation x^2-18=7*x
-
Equation x^2+9=0
-
Equation -7x=4
- Express {x} in terms of y where:
- 17*x-19*y=-12
- 13*x-1*y=-20
- -6*x-11*y=-20
- -15*x+7*y=1
- Derivative of:
-
cos(x-pi/6)
- Graphing y =:
- cos(x-pi/6)
-
Identical expressions
- cos(x-pi/ six)= one
- co sinus of e of (x minus Pi divide by 6) equally 1
- co sinus of e of (x minus Pi divide by six) equally one
- cosx-pi/6=1
- cos(x-pi divide by 6)=1
-
Similar expressions
- cos(x+pi/6)=1
- cos(x-(pi/6))=-1/2
cos(x-pi/6)=1 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$\cos{\left(x - \frac{\pi}{6} \right)} = 1$$
- this is the simplest trigonometric equation
This equation is transformed to
$$x + \frac{\pi}{3} = 2 \pi n + \operatorname{asin}{\left(1 \right)}$$
$$x + \frac{\pi}{3} = 2 \pi n - \operatorname{asin}{\left(1 \right)} + \pi$$
Or
$$x + \frac{\pi}{3} = 2 \pi n + \frac{\pi}{2}$$
$$x + \frac{\pi}{3} = 2 \pi n + \frac{\pi}{2}$$
, where n - is a integer
Move
$$\frac{\pi}{3}$$
to right part of the equation
with the opposite sign, in total:
$$x = 2 \pi n + \frac{\pi}{6}$$
$$x = 2 \pi n + \frac{\pi}{6}$$
$$\cos{\left(x - \frac{\pi}{6} \right)} = 1$$
- this is the simplest trigonometric equation
This equation is transformed to
$$x + \frac{\pi}{3} = 2 \pi n + \operatorname{asin}{\left(1 \right)}$$
$$x + \frac{\pi}{3} = 2 \pi n - \operatorname{asin}{\left(1 \right)} + \pi$$
Or
$$x + \frac{\pi}{3} = 2 \pi n + \frac{\pi}{2}$$
$$x + \frac{\pi}{3} = 2 \pi n + \frac{\pi}{2}$$
, where n - is a integer
Move
$$\frac{\pi}{3}$$
to right part of the equation
with the opposite sign, in total:
$$x = 2 \pi n + \frac{\pi}{6}$$
$$x = 2 \pi n + \frac{\pi}{6}$$
Sum and product of roots
[src]
sum
pi -- 6
$$\frac{\pi}{6}$$
=
pi -- 6
$$\frac{\pi}{6}$$
product
pi -- 6
$$\frac{\pi}{6}$$
=
pi -- 6
$$\frac{\pi}{6}$$
pi/6
Numerical answer
[src]
x1 = 69.6386373706038
x2 = 57.0722669678592
x3 = -12.0427717972535
x4 = -12.0427723286991
x5 = 44.5058964424528
x6 = -56.025069474968
x7 = -100.007366130816
x8 = 25.6563394682159
x9 = -93.7241808502169
x10 = 82.2050073898185
x11 = 82.2050082364122
x12 = -49.7418836877515
x13 = -37.1755133514019
x14 = -43.4586978581934
x15 = 94.7713788787456
x16 = 75.9218225293406
x17 = 31.9395248180032
x18 = -56.0250686737045
x19 = -56.0250689627851
x20 = 75.921822712036
x21 = 101.054563320377
x22 = -5.75958688099515
x23 = 6.80678380605397
x24 = 63.3554521807345
x25 = -87.4409951626836
x26 = 75.9218219651159
x27 = 0.523599292248804
x28 = 38.2227106406115
x29 = 50.7890817256271
x30 = -93.7241803428761
x31 = -24.6091429188071
x32 = 25.6563402122788
x33 = -5.75958605222168
x34 = -12.0427715433223
x35 = 69.6386366502817
x36 = -93.7241811464116
x37 = 31.9395255853156
x38 = -30.8923281481345
x39 = 107.33774924983
x40 = 1148089.27566767
x41 = -5.75958652427977
x42 = 44.5058960754604
x43 = 19.373155023778
x44 = -43.4586992463883
x45 = -74.8746244986124
x46 = -18.3259569461439
x47 = 69.6386365178538
x48 = -62.3082546549224
x49 = -62.3082548040693
x50 = 31.939525366622
x51 = -81.1578097346531
x52 = -49.7418840144382
x53 = 50.7890809635851
x54 = -62.3082541046692
x55 = -43.4586985346108
x56 = -49.7418831973114
x57 = -12.0427731031181
x58 = -74.8746253041062
x59 = -37.1755125810757
x60 = 13.0899706264067
x61 = -24.6091421332653
x62 = -30.8923273430118
x63 = 94.7713781211905
x64 = 38.2227110923636
x65 = 44.5058957827896
x66 = 88.4881935924098
x67 = 13.0899690079379
x68 = 88.4881931672644
x69 = -68.5914400728566
x70 = -87.4409950088659
x71 = -100.007365805676
x72 = 88.4881929416299
x73 = 57.0722661641091
x74 = 6.80678457235213
x75 = 19.3731542353829
x76 = 82.2050078076022
x77 = -18.3259575894274
x78 = 0.523598989487319
x79 = -43.4586980900846
x80 = 25.6563394986191
x81 = 13.0899698124794
x82 = 38.222710253794
x83 = 38.2227096146998
x84 = -18.3259576528335
x85 = -87.440995693181
x86 = 63.3554513897102
x87 = -81.1578105087816
x88 = 0.523598624044635
x89 = -68.5914392903944
x89 = -68.5914392903944