Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation cos(x)=sqrt(3)/2
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Equation x^2-8x+15=0
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Equation 5-2*(x-1)=4-x
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Equation (x-2)^2=(x-9)^2
- Express {x} in terms of y where:
- -6*x-2*y=-10
- -10*x+9*y=-6
- -14*x-16*y=14
- 20*x-4*y=-7
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Identical expressions
- two cosx-√2= zero
- 2 co sinus of e of x minus √2 equally 0
- two co sinus of e of x minus √2 equally zero
- 2cosx-√2=O
-
Similar expressions
- 2cosx+√2=0
2cosx-√2=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$2 \cos{\left(x \right)} - \sqrt{2} = 0$$
- this is the simplest trigonometric equation
We get:
$$2 \cos{\left(x \right)} = \sqrt{2}$$
The equation is transformed to
$$\cos{\left(x \right)} = \frac{\sqrt{2}}{2}$$
This equation is transformed to
$$x = \pi n + \operatorname{acos}{\left(\frac{\sqrt{2}}{2} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(\frac{\sqrt{2}}{2} \right)}$$
Or
$$x = \pi n + \frac{\pi}{4}$$
$$x = \pi n - \frac{3 \pi}{4}$$
, where n - is a integer
$$2 \cos{\left(x \right)} - \sqrt{2} = 0$$
- this is the simplest trigonometric equation
Move -sqrt(2) to right part of the equation
with the change of sign in -sqrt(2)
We get:
$$2 \cos{\left(x \right)} = \sqrt{2}$$
Divide both parts of the equation by 2
The equation is transformed to
$$\cos{\left(x \right)} = \frac{\sqrt{2}}{2}$$
This equation is transformed to
$$x = \pi n + \operatorname{acos}{\left(\frac{\sqrt{2}}{2} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(\frac{\sqrt{2}}{2} \right)}$$
Or
$$x = \pi n + \frac{\pi}{4}$$
$$x = \pi n - \frac{3 \pi}{4}$$
, where n - is a integer
Rapid solution
[src]
pi
x1 = --
4
$$x_{1} = \frac{\pi}{4}$$
7*pi
x2 = ----
4
$$x_{2} = \frac{7 \pi}{4}$$
x2 = 7*pi/4
Sum and product of roots
[src]
sum
pi 7*pi -- + ---- 4 4
$$\frac{\pi}{4} + \frac{7 \pi}{4}$$
=
2*pi
$$2 \pi$$
product
pi 7*pi --*---- 4 4
$$\frac{\pi}{4} \frac{7 \pi}{4}$$
=
2 7*pi ----- 16
$$\frac{7 \pi^{2}}{16}$$
7*pi^2/16
Numerical answer
[src]
x1 = 0.785398163397448
x2 = -55.7632696012188
x3 = -82.4668071567321
x4 = 24.3473430653209
x5 = -101.316363078271
x6 = -69.9004365423729
x7 = -43.1968989868597
x8 = 76.1836218495525
x9 = -62.0464549083984
x10 = 93.4623814442964
x11 = -51.0508806208341
x12 = 36.9137136796801
x13 = 74.6128255227576
x14 = 51.0508806208341
x15 = -49.4800842940392
x16 = 87.1791961371168
x17 = 19.6349540849362
x18 = 5.49778714378214
x19 = -36.9137136796801
x20 = -162.577419823272
x21 = 43.1968989868597
x22 = -24.3473430653209
x23 = -13.3517687777566
x24 = 82.4668071567321
x25 = 18.0641577581413
x26 = -74.6128255227576
x27 = 11.7809724509617
x28 = 69.9004365423729
x29 = 32.2013246992954
x30 = 57.3340659280137
x31 = 99.7455667514759
x32 = -182.997772071605
x33 = 88.7499924639117
x34 = -93.4623814442964
x35 = -7.06858347057703
x36 = -87.1791961371168
x37 = 55.7632696012188
x38 = -351.072979038659
x39 = -99.7455667514759
x40 = -63.6172512351933
x41 = 95.0331777710912
x42 = -38.484510006475
x43 = 38.484510006475
x44 = -32.2013246992954
x45 = 30.6305283725005
x46 = -0.785398163397448
x47 = -5.49778714378214
x48 = -80.8960108299372
x49 = -68.329640215578
x50 = 49.4800842940392
x51 = -88.7499924639117
x52 = 7.06858347057703
x53 = -95.0331777710912
x54 = -11.7809724509617
x55 = -76.1836218495525
x56 = 44.7676953136546
x57 = -44.7676953136546
x58 = -30.6305283725005
x59 = 63.6172512351933
x60 = 62.0464549083984
x61 = 25.9181393921158
x62 = -18.0641577581413
x63 = -57.3340659280137
x64 = -25.9181393921158
x65 = 68.329640215578
x66 = 80.8960108299372
x67 = -19.6349540849362
x68 = 13.3517687777566
x68 = 13.3517687777566