Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation x-6/x=-1
-
Equation cos(x)-1/2=0
-
Equation tg(x)=0
- Equation x^5-32=0
- Express {x} in terms of y where:
- -14*x+1*y=3
- -11*x+4*y=-8
- 16*x+7*y=8
- 17*x-11*y=2
- Integral of d{x}:
- cos(x)-1/2
- Graphing y =:
- cos(x)-1/2
-
Identical expressions
- cos(x)- one / two = zero
- co sinus of e of (x) minus 1 divide by 2 equally 0
- co sinus of e of (x) minus one divide by two equally zero
- cosx-1/2=0
- cos(x)-1/2=O
- cos(x)-1 divide by 2=0
-
Similar expressions
- (cos(x-1/2))*(sin(x+1))=0
- 3^-2/2*cosx-1/2*sinx=1
- cos(x)+1/2=0
- cosx-1/2=0
cos(x)-1/2=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$\cos{\left(x \right)} - \frac{1}{2} = 0$$
- this is the simplest trigonometric equation
We get:
$$\cos{\left(x \right)} - \frac{1}{2} + \frac{1}{2} = \frac{1}{2}$$
This equation is transformed to
$$x = \pi n + \operatorname{acos}{\left(\frac{1}{2} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(\frac{1}{2} \right)}$$
Or
$$x = \pi n + \frac{\pi}{3}$$
$$x = \pi n - \frac{2 \pi}{3}$$
, where n - is a integer
$$\cos{\left(x \right)} - \frac{1}{2} = 0$$
- this is the simplest trigonometric equation
Move -1/2 to right part of the equation
with the change of sign in -1/2
We get:
$$\cos{\left(x \right)} - \frac{1}{2} + \frac{1}{2} = \frac{1}{2}$$
This equation is transformed to
$$x = \pi n + \operatorname{acos}{\left(\frac{1}{2} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(\frac{1}{2} \right)}$$
Or
$$x = \pi n + \frac{\pi}{3}$$
$$x = \pi n - \frac{2 \pi}{3}$$
, where n - is a integer
Sum and product of roots
[src]
sum
pi 5*pi -- + ---- 3 3
$$\left(\frac{\pi}{3}\right) + \left(\frac{5 \pi}{3}\right)$$
=
2*pi
$$2 \pi$$
product
pi 5*pi -- * ---- 3 3
$$\left(\frac{\pi}{3}\right) * \left(\frac{5 \pi}{3}\right)$$
=
2 5*pi ----- 9
$$\frac{5 \pi^{2}}{9}$$
Rapid solution
[src]
pi
x_1 = --
3
$$x_{1} = \frac{\pi}{3}$$
5*pi
x_2 = ----
3
$$x_{2} = \frac{5 \pi}{3}$$
Numerical answer
[src]
x1 = -93.2005820564972
x2 = 24.0855436775217
x3 = 55.5014702134197
x4 = 89.0117918517108
x5 = -26.1799387799149
x6 = -61.7846555205993
x7 = -55.5014702134197
x8 = -51.3126800086333
x9 = -95.2949771588904
x10 = -11.5191730631626
x11 = -63.8790506229925
x12 = 86.9173967493176
x13 = 30.3687289847013
x14 = 63.8790506229925
x15 = 95.2949771588904
x16 = 7.33038285837618
x17 = 19.8967534727354
x18 = 51.3126800086333
x19 = 45.0294947014537
x20 = 13.6135681655558
x21 = 26.1799387799149
x22 = 49.2182849062401
x23 = 1.0471975511966
x24 = 68.0678408277789
x25 = -7.33038285837618
x26 = -17.8023583703422
x27 = -30.3687289847013
x28 = -1.0471975511966
x29 = -80.634211442138
x30 = -49.2182849062401
x31 = -225.147473507269
x32 = 32.4631240870945
x33 = -45.0294947014537
x34 = -74.3510261349584
x35 = 70.162235930172
x36 = 93.2005820564972
x37 = -5.23598775598299
x38 = -89.0117918517108
x39 = 42.9350995990605
x40 = -13.6135681655558
x41 = -32.4631240870945
x42 = -42.9350995990605
x43 = -38.7463093942741
x44 = -24.0855436775217
x45 = 80.634211442138
x46 = 11.5191730631626
x47 = 82.7286065445312
x48 = -70.162235930172
x49 = -99.4837673636768
x50 = 5.23598775598299
x51 = -36.6519142918809
x52 = 38.7463093942741
x53 = -359.188760060433
x54 = -57.5958653158129
x55 = -68.0678408277789
x56 = 61.7846555205993
x57 = -82.7286065445312
x58 = 17.8023583703422
x59 = -76.4454212373516
x60 = -19.8967534727354
x61 = 76.4454212373516
x62 = 57.5958653158129
x63 = -86.9173967493176
x64 = 74.3510261349584
x65 = 99.4837673636768
x66 = 1651.43053823704
x67 = 36.6519142918809
x67 = 36.6519142918809
The graph