Question

TRUE or FALSE?

The sine function is an odd function.

Answer 1

for odd function, f(x) = -f(-x)
so is it true that sin (-x) = -sin x ?

Answer 2

Is it true because:

sin(z) = z - z^3/3! + z^5/5! - ... Odd powers and factorials

cos(z) = 1 - z^2/2 + z^4/4! - ... Even powers and factorials

Answer 3

yes, that could be another reasoning too, that sin has odd powers only

Answer 4

Oh i see your equations at the top! Thanks

Answer 5

welcome ^_^

Answer 6

Actually, can you help me with one more? @hartnn @satellite73

Answer 7

a more prosaic way to see the same thing

Answer 8

Which natural phenomenon is the best example of periodic behavior?
A. The number of fish in a pond as a function of time
B. The number of hours of daylight each day
C. The closing value of the stock market at the end of each day
D. The amount of pollution in Los Angeles as a function of time

Answer 9

i would go with B
days get longer, days get shorter
longer
shorter
longer
shorter ...

Answer 10

periodic behaivour means that function keeps on repeating at equal intervals
like f(x) = f(x+n)

Answer 11

Oh! I see now @satellite73 ! Thank for giving a visual

Answer 12

Got it! B. The number of hours of daylight each day

Thank you both!