Mister Exam
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How to use it?
- Equation:
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Equation -4x=15-3(3x-5)
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Equation 9x−9(x+1)=−2x
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Equation -25-x=-17
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Equation z^4+16=0
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Identical expressions
- cos(x/ two -Pi/ eight)= zero
- co sinus of e of (x divide by 2 minus Pi divide by 8) equally 0
- co sinus of e of (x divide by two minus Pi divide by eight) equally zero
- cosx/2-Pi/8=0
- cos(x/2-Pi/8)=O
- cos(x divide by 2-Pi divide by 8)=0
-
Similar expressions
- cos(x/2+Pi/8)=0
cos(x/2-Pi/8)=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
/x pi\ cos|- - --| = 0 \2 8 /
$$\cos{\left(\frac{x}{2} - \frac{\pi}{8} \right)} = 0$$
Detail solution
Given the equation
$$\cos{\left(\frac{x}{2} - \frac{\pi}{8} \right)} = 0$$
- this is the simplest trigonometric equation
We get:
$$\cos{\left(\frac{x}{2} - \frac{\pi}{8} \right)} = 0$$
This equation is transformed to
$$\frac{x}{2} + \frac{3 \pi}{8} = 2 \pi n + \operatorname{asin}{\left(0 \right)}$$
$$\frac{x}{2} + \frac{3 \pi}{8} = 2 \pi n - \operatorname{asin}{\left(0 \right)} + \pi$$
Or
$$\frac{x}{2} + \frac{3 \pi}{8} = 2 \pi n$$
$$\frac{x}{2} + \frac{3 \pi}{8} = 2 \pi n + \pi$$
, where n - is a integer
Move
$$\frac{3 \pi}{8}$$
to right part of the equation
with the opposite sign, in total:
$$\frac{x}{2} = 2 \pi n - \frac{3 \pi}{8}$$
$$\frac{x}{2} = 2 \pi n + \frac{5 \pi}{8}$$
Divide both parts of the equation by
$$\frac{1}{2}$$
we get the answer:
$$x_{1} = 4 \pi n - \frac{3 \pi}{4}$$
$$x_{2} = 4 \pi n + \frac{5 \pi}{4}$$
$$\cos{\left(\frac{x}{2} - \frac{\pi}{8} \right)} = 0$$
- this is the simplest trigonometric equation
with the change of sign in 0
We get:
$$\cos{\left(\frac{x}{2} - \frac{\pi}{8} \right)} = 0$$
This equation is transformed to
$$\frac{x}{2} + \frac{3 \pi}{8} = 2 \pi n + \operatorname{asin}{\left(0 \right)}$$
$$\frac{x}{2} + \frac{3 \pi}{8} = 2 \pi n - \operatorname{asin}{\left(0 \right)} + \pi$$
Or
$$\frac{x}{2} + \frac{3 \pi}{8} = 2 \pi n$$
$$\frac{x}{2} + \frac{3 \pi}{8} = 2 \pi n + \pi$$
, where n - is a integer
Move
$$\frac{3 \pi}{8}$$
to right part of the equation
with the opposite sign, in total:
$$\frac{x}{2} = 2 \pi n - \frac{3 \pi}{8}$$
$$\frac{x}{2} = 2 \pi n + \frac{5 \pi}{8}$$
Divide both parts of the equation by
$$\frac{1}{2}$$
we get the answer:
$$x_{1} = 4 \pi n - \frac{3 \pi}{4}$$
$$x_{2} = 4 \pi n + \frac{5 \pi}{4}$$
Rapid solution
[src]
-3*pi
x1 = -----
4
$$x_{1} = - \frac{3 \pi}{4}$$
5*pi
x2 = ----
4
$$x_{2} = \frac{5 \pi}{4}$$
x2 = 5*pi/4
Sum and product of roots
[src]
sum
3*pi 5*pi - ---- + ---- 4 4
$$- \frac{3 \pi}{4} + \frac{5 \pi}{4}$$
=
pi -- 2
$$\frac{\pi}{2}$$
product
-3*pi 5*pi -----*---- 4 4
$$- \frac{3 \pi}{4} \frac{5 \pi}{4}$$
=
2 -15*pi ------- 16
$$- \frac{15 \pi^{2}}{16}$$
-15*pi^2/16
Numerical answer
[src]
x1 = -65.1880475619882
x2 = 47.9092879672443
x3 = -8.63937979737193
x4 = -40.0553063332699
x5 = 3.92699081698724
x6 = 29.0597320457056
x7 = -102.887159405066
x8 = -33.7721210260903
x9 = -58.9048622548086
x10 = 98.174770424681
x11 = 35.3429173528852
x12 = 85.6083998103219
x13 = -27.4889357189107
x14 = 54.1924732744239
x15 = -84.037603483527
x16 = 10.2101761241668
x17 = 41.6261026600648
x18 = -115.453530019425
x19 = 79.3252145031423
x20 = -14.9225651045515
x21 = -46.3384916404494
x22 = -96.6039740978861
x23 = 60.4756585816035
x24 = -153.152641862502
x25 = -90.3207887907066
x26 = 22.776546738526
x27 = -2.35619449019234
x28 = -71.4712328691678
x29 = -52.621676947629
x30 = 66.7588438887831
x31 = 91.8915851175014
x32 = -21.2057504117311
x33 = 73.0420291959627
x34 = 16.4933614313464
x35 = -77.7544181763474
x35 = -77.7544181763474