Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation x^2=49
-
Equation cos(pi*(x-1)/3)=1/2
-
Equation 3*x^2-3=0
-
Equation 5(7x+3)-12=4(9x-6)
- Express {x} in terms of y where:
- 18*x-14*y=-12
- 4*x-18*y=-14
- -14*x-1*y=3
- 10*x-18*y=6
- Graphing y =:
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tan(x/2)
- Integral of d{x}:
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tan(x/2)
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-1
- Limit of the function:
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tan(x/2)
- Sum of series:
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-1
- Derivative of:
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-1
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Identical expressions
- tan(x/ two)=- one
- tangent of (x divide by 2) equally minus 1
- tangent of (x divide by two) equally minus one
- tanx/2=-1
- tan(x divide by 2)=-1
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Similar expressions
- tanx/2=√3/2
- tan(x/2)=+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 = -76.9690200129499
x2 = -70.6858347057703
x3 = 86.3937979737193
x4 = 42.4115008234622
x5 = -39.2699081698724
x6 = -89.5353906273091
x7 = -58.1194640914112
x8 = -32.9867228626928
x9 = -83.2522053201295
x10 = 92.6769832808989
x11 = -20.4203522483337
x12 = 61.261056745001
x13 = -51.8362787842316
x14 = 98.9601685880785
x15 = -102.101761241668
x16 = -14.1371669411541
x17 = 67.5442420521806
x18 = -26.7035375555132
x19 = -64.4026493985908
x20 = -1.5707963267949
x21 = 23.5619449019235
x22 = 17.2787595947439
x23 = -95.8185759344887
x24 = 10.9955742875643
x25 = 36.1283155162826
x26 = 48.6946861306418
x27 = 80.1106126665397
x28 = 4.71238898038469
x29 = -7.85398163397448
x30 = 73.8274273593601
x31 = 29.845130209103
x32 = -45.553093477052
x33 = 54.9778714378214
x33 = 54.9778714378214
The graph