Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation (4x-6)-(9x-4)=18
- Equation tg(pix/12)=-1
- Equation sin(-t/4)=-sqrt(2)/2
-
Equation 3x-9/x-1+x+6/x+1=3
- Express {x} in terms of y where:
- -18*x-1*y=-11
- 14*x+16*y=-3
- 2*x-15*y=-1
- 12*x-14*y=20
- Sum of series:
-
-1
- Integral of d{x}:
-
-1
- Derivative of:
-
-1
-
Identical expressions
- tg(pix/ twelve)=- one
- tg( Pi x divide by 12) equally minus 1
- tg( Pi x divide by twelve) equally minus one
- tgpix/12=-1
- tg(pix divide by 12)=-1
-
Similar expressions
- tg(pix/12)=+1
tg(pix/12)=-1 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$\tan{\left(\frac{\pi x}{12} \right)} = -1$$
- this is the simplest trigonometric equation
This equation is transformed to
$$\frac{\pi x}{12} = \pi n + \operatorname{atan}{\left(-1 \right)}$$
Or
$$\frac{\pi x}{12} = \pi n - \frac{\pi}{4}$$
, where n - is a integer
Divide both parts of the equation by
$$\frac{\pi}{12}$$
we get the answer:
$$x_{1} = \frac{12 \left(\pi n - \frac{\pi}{4}\right)}{\pi}$$
$$\tan{\left(\frac{\pi x}{12} \right)} = -1$$
- this is the simplest trigonometric equation
This equation is transformed to
$$\frac{\pi x}{12} = \pi n + \operatorname{atan}{\left(-1 \right)}$$
Or
$$\frac{\pi x}{12} = \pi n - \frac{\pi}{4}$$
, where n - is a integer
Divide both parts of the equation by
$$\frac{\pi}{12}$$
we get the answer:
$$x_{1} = \frac{12 \left(\pi n - \frac{\pi}{4}\right)}{\pi}$$
Numerical answer
[src]
x1 = -51.0
x2 = 45.0
x3 = 33.0
x4 = -99.0
x5 = 57.0
x6 = -27.0
x7 = 81.0
x8 = 9.0
x9 = -75.0
x10 = -3.0
x11 = -15.0
x12 = -39.0
x13 = 93.0
x14 = -87.0
x15 = 21.0
x16 = 69.0
x17 = -63.0
x17 = -63.0