Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation 4x+2(1-3x)=13
-
Equation x^2-10x+25=0
- Equation x-y=0
-
Equation 3-x=1+x
- Express {x} in terms of y where:
- -2*x-4*y=11
- 14*x-3*y=-9
- 6*x-19*y=-18
- 10*x-5*y=3
- Derivative of:
-
cos2x
- Integral of d{x}:
-
cos2x
- Graphing y =:
- cos2x
-
Identical expressions
- cos two x=-(√ two /2)
- co sinus of e of 2x equally minus (√2 divide by 2)
- co sinus of e of two x equally minus (√ two divide by 2)
- cos2x=-√2/2
- cos2x=-(√2 divide by 2)
-
Similar expressions
- cos2x=+(√2/2)
- 2*sin^2x+3cos^2x+2sinx=0
- sin(2x/7)=-√2/2
- 2*cos(2*x)+4*sqrt(3)*cos(x)-7=0
- sin(6x+пи)=-√2/2
- cos=-√2/2
- 2*cos(2*x)-1=0
- sin2x+16cos^2x=4
cos2x=-(√2/2) equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
___
-\/ 2
cos(2*x) = -------
2
$$\cos{\left(2 x \right)} = - \frac{\sqrt{2}}{2}$$
Detail solution
Given the equation
$$\cos{\left(2 x \right)} = - \frac{\sqrt{2}}{2}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$2 x = \pi n + \operatorname{acos}{\left(- \frac{\sqrt{2}}{2} \right)}$$
$$2 x = \pi n - \pi + \operatorname{acos}{\left(- \frac{\sqrt{2}}{2} \right)}$$
Or
$$2 x = \pi n + \frac{3 \pi}{4}$$
$$2 x = \pi n - \frac{\pi}{4}$$
, where n - is a integer
Divide both parts of the equation by
$$2$$
we get the answer:
$$x_{1} = \frac{\pi n}{2} + \frac{3 \pi}{8}$$
$$x_{2} = \frac{\pi n}{2} - \frac{\pi}{8}$$
$$\cos{\left(2 x \right)} = - \frac{\sqrt{2}}{2}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$2 x = \pi n + \operatorname{acos}{\left(- \frac{\sqrt{2}}{2} \right)}$$
$$2 x = \pi n - \pi + \operatorname{acos}{\left(- \frac{\sqrt{2}}{2} \right)}$$
Or
$$2 x = \pi n + \frac{3 \pi}{4}$$
$$2 x = \pi n - \frac{\pi}{4}$$
, where n - is a integer
Divide both parts of the equation by
$$2$$
we get the answer:
$$x_{1} = \frac{\pi n}{2} + \frac{3 \pi}{8}$$
$$x_{2} = \frac{\pi n}{2} - \frac{\pi}{8}$$
Sum and product of roots
[src]
sum
3*pi 5*pi ---- + ---- 8 8
$$\frac{3 \pi}{8} + \frac{5 \pi}{8}$$
=
pi
$$\pi$$
product
3*pi 5*pi ----*---- 8 8
$$\frac{3 \pi}{8} \frac{5 \pi}{8}$$
=
2 15*pi ------ 64
$$\frac{15 \pi^{2}}{64}$$
15*pi^2/64
Rapid solution
[src]
3*pi
x1 = ----
8
$$x_{1} = \frac{3 \pi}{8}$$
5*pi
x2 = ----
8
$$x_{2} = \frac{5 \pi}{8}$$
x2 = 5*pi/8
Numerical answer
[src]
x1 = 33.3794219443916
x2 = 17.6714586764426
x3 = -99.3528676697772
x4 = 99.3528676697772
x5 = -92.2842841992002
x6 = 67.9369411338793
x7 = -54.5851723561227
x8 = -49.0873852123405
x9 = -48.3019870489431
x10 = -13.7444678594553
x11 = 86.0010988920206
x12 = 64.009950316892
x13 = -33.3794219443916
x14 = 98.5674695063798
x15 = -1.96349540849362
x16 = 1.96349540849362
x17 = -55.3705705195201
x18 = -32.5940237809941
x19 = 249.36391687869
x20 = -96.2112750161874
x21 = -79.717913584841
x22 = -76.5763209312512
x23 = -86.0010988920206
x24 = -35.7356164345839
x25 = 52.2289778659303
x26 = -89.9280897090078
x27 = -61.6537558266997
x28 = -98.5674695063798
x29 = 45.9457925587507
x30 = -11.388273369263
x31 = -64.009950316892
x32 = 11.388273369263
x33 = 38.8772090881737
x34 = -67.9369411338793
x35 = -30.2378292908018
x36 = 74.2201264410589
x37 = -39.6626072515711
x38 = -117.417025427919
x39 = 48.3019870489431
x40 = 70.2931356240716
x41 = 54.5851723561227
x42 = 32.5940237809941
x43 = 20.0276531666349
x44 = -10.6028752058656
x45 = 8.24668071567321
x46 = 42.0188017417635
x47 = -26.3108384738145
x48 = -77.3617190946487
x49 = 77.3617190946487
x50 = -20.0276531666349
x51 = 96.2112750161874
x52 = -57.7267650097125
x53 = 3529.97204538983
x54 = -23.9546439836222
x55 = 55.3705705195201
x56 = 30.2378292908018
x57 = -93.0696823625976
x58 = 76.5763209312512
x59 = -83.6449044018282
x60 = 57.7267650097125
x61 = 61.6537558266997
x62 = -4.31968989868597
x63 = -52.2289778659303
x64 = -17.6714586764426
x65 = -27.096236637212
x66 = 10.6028752058656
x67 = -74.2201264410589
x68 = 60.8683576633022
x69 = -70.2931356240716
x70 = 16.8860605130451
x71 = 92.2842841992002
x72 = 83.6449044018282
x73 = 39.6626072515711
x74 = -71.0785337874691
x75 = 23.9546439836222
x76 = -126.841803388688
x77 = -42.0188017417635
x78 = -45.9457925587507
x79 = 4.31968989868597
x80 = 82.8595062384308
x81 = -224.231175649972
x82 = 89.9280897090078
x83 = 26.3108384738145
x84 = -5.10508806208341
x84 = -5.10508806208341