Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation 3x=2
-
Equation -5+9x=10x+4
-
Equation 25*x^3-10*x^2+x=0
-
Equation x^2+7x=18
- Express {x} in terms of y where:
- -16*x+14*y=-9
- 11*x-2*y=-9
- 15*x+12*y=-19
- -19*x-20*y=-4
- Graphing y =:
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tan(x/2)
- Integral of d{x}:
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tan(x/2)
- Limit of the function:
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tan(x/2)
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Identical expressions
- tan(x/ two)= one
- tangent of (x divide by 2) equally 1
- tangent of (x divide by two) equally one
- tanx/2=1
- tan(x divide by 2)=1
-
Similar expressions
- tan(x/2-pi/5)=1
tan(x/2)=1 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$\tan{\left(\frac{x}{2} \right)} = 1$$
- this is the simplest trigonometric equation
This equation is transformed to
$$\frac{x}{2} = \pi n + \operatorname{atan}{\left(1 \right)}$$
Or
$$\frac{x}{2} = \pi n + \frac{\pi}{4}$$
, where n - is a integer
Divide both parts of the equation by
$$\frac{1}{2}$$
we get the answer:
$$x_{1} = 2 \pi n + \frac{\pi}{2}$$
$$\tan{\left(\frac{x}{2} \right)} = 1$$
- this is the simplest trigonometric equation
This equation is transformed to
$$\frac{x}{2} = \pi n + \operatorname{atan}{\left(1 \right)}$$
Or
$$\frac{x}{2} = \pi n + \frac{\pi}{4}$$
, where n - is a integer
Divide both parts of the equation by
$$\frac{1}{2}$$
we get the answer:
$$x_{1} = 2 \pi n + \frac{\pi}{2}$$
Sum and product of roots
[src]
sum
pi -- 2
$$\frac{\pi}{2}$$
=
pi -- 2
$$\frac{\pi}{2}$$
product
pi -- 2
$$\frac{\pi}{2}$$
=
pi -- 2
$$\frac{\pi}{2}$$
pi/2
Numerical answer
[src]
x1 = 102.101761241668
x2 = -17.2787595947439
x3 = 95.8185759344887
x4 = -4.71238898038469
x5 = 76.9690200129499
x6 = -36.1283155162826
x7 = -23.5619449019235
x8 = -61.261056745001
x9 = -92.6769832808989
x10 = 1.5707963267949
x11 = 64.4026493985908
x12 = 20.4203522483337
x13 = 26.7035375555132
x14 = -42.4115008234622
x15 = 32.9867228626928
x16 = -29.845130209103
x17 = 70.6858347057703
x18 = -10.9955742875643
x19 = -80.1106126665397
x20 = 83.2522053201295
x21 = -73.8274273593601
x22 = 45.553093477052
x23 = -48.6946861306418
x24 = 51.8362787842316
x25 = 58.1194640914112
x26 = 39.2699081698724
x27 = -54.9778714378214
x28 = -86.3937979737193
x29 = 7.85398163397448
x30 = 14.1371669411541
x31 = -98.9601685880785
x32 = 89.5353906273091
x33 = -67.5442420521806
x33 = -67.5442420521806
The graph