Question

sin 7pi/3

Answer 1

sin(x) = sin(x ± 2pi)

7pi/3 - 2pi = pi/3

therefore sin(7pi/3) = sin(pi/3)

Answer 2

can you explain this briefly ? @Euler271

Answer 3

because in the book they mention reference numbers

Answer 4

idk what reference numbers they are talking about; maybe the unit circle.

but it is just because sin(x) and cos(x) are periodic functions, meaning functions that continuously repeat themselves. the property of a periodic function is that f(x + T) = f(x), where T is the period.

Answer 5

okay. i see how about csc 7pi/3

Answer 6

csc(x) = 1/sin(x). best to find sin(x) first usually then take the inverse

Answer 7

for the 1st problem how did you know to subtract 2 pi?? what logic are you using im confused on that part ?

Answer 8

because it's a periodic function with a period of T = 2pi

and f(x ± T) = f(x) for any periodic function

so its equivalent to sin(pi/3) which is sqrt(3) / 2

Answer 9

okay. for the second one find sin X and take the inverse how ?

Answer 10

inverse as in: \[\csc x = \frac{ 1 }{ \sin x }\]