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I typed an Trigonometric equation to be solved by the calculator i think it was: sin45= cosβ, i was expecting 45 β.
But no...
I was shocked when i saw that β=10000035.
Do anyone have any explanation?
I tried cos10000035 it gave me sqrt(2)/2 like the sine and cosine of 45.
And sin10000035 gave -sqrt(2)/2 that is -sin45 and -cos45.
In addition, I noticed that 10000035 is a base of an angle system like 45 is the base of DEGREES.
Because sin10000034=-cos10000036, notice the negative form of the other trig function.
What do you think guys?
N.B: My calculator was set in DEG mode and not other modes, and i'm pretty sure it has nothing to do with my calculator.
I knew the modulo operator used it many times in python algorithms but whats wrong with 10000035
10000035 % 360
what's so weird about it ?
Solution I:

sin (45) = cos(β) = sin(pi/2 + β)

=> pi/2 + β = 45 + 2kpi
or pi - (pi/2 + β) = 45 + 2kpi (where k is an integer)

=> β = 45 - pi/2 + 2kpi = -45 + 2kpi (solution set A)
or β = pi - pi/2 - 45 - 2kpi = 45 + 2kpi (solution set B)

Solution II:

sin(45) = cos(β) = sin (pi/2 - β)

=> pi/2 - β = 45 + 2kpi
or pi - (pi/2 - β) = 45 + 2kpi (where k is an integer)

=> β = pi/2 - 45 - 2kpi = 45 + 2kpi (solution set B)
or β = 45 - pi + pi/2 + 2kpi = -45 + 2kpi (solution set A)

So β is a modulo of -45 degrees if it belongs to solution set A or 45 degrees if it belongs to solution set B

For β = 10000035, β is a solution of set B since 10000035 = -45 + 2kpi => k = 27778
mesa177 wrotesin (45) = cos(β) = sin(pi/2 + β)

pi/2 + β = 45 + 2kpi
β = 45 - pi/2 + 2kpi = -45 + 2kpi

So β is a modulo of -45 degrees and not 45 degrees

For β = 10000035, 10000035 = -45 + 2kpi => k = 27778
Pretty good, thanks mate.
I hope I can print this in my memory for future uses.

Anyway, can anyone explain this e^(j*pi)=-1 where j is a complex number, we all know pi and e the constant of Euler.
NuclearVision wroteAnyway, can anyone explain this e^(j*pi)=-1 where j is a complex number, we all know pi and e the constant of Euler.
Every complex number Z has an equivalent exponential form where Z = r*e^(j*θ), but complex numbers also are expressed in rectangular coordinates where Z = x + j*y

=> x + j*y = r*e^(j*θ) which of course leads to the polar coordinates:

x = r*cos(θ)
y = r*sin(θ)

In the case given, r = 1 and θ = pi

=> x = cos(pi) = -1
y = sin(pi) = 0

=> Z = -1 = e^(j*pi)
NuclearVision wrotePretty good, thanks man.
Guess again ;)
mesa177 wrote
NuclearVision wroteAnyway, can anyone explain this e^(j*pi)=-1 where j is a complex number, we all know pi and e the constant of Euler.
Every complex number Z has an equivalent exponential form where Z = r*e^(j*θ), but complex numbers also are expressed in rectangular coordinates where Z = x + j*y

=> x + j*y = r*e^(j*θ) which of course leads to the polar coordinates:

x = r*cos(θ)
y = r*sin(θ)

In the case given, r = 1 and θ = pi

=> x = cos(pi) = -1
y = sin(pi) = 0

=> Z = -1 = e^(j*pi)
NuclearVision wrotePretty good, thanks man.
Guess again ;)
Thanks again, mate***.