SOLUTION: Please help me solve this question. Let g : N -> {+-cos(x), +-sin(x)} be defined by {{{g(n)=(d^(n)/dx^(n))sin(x)}}} a)Find a description of g(n) without using the differen

Question 735077: Please help me solve this question.
Let g : N -> {+-cos(x), +-sin(x)} be defined by

a)Find a description of g(n) without using the differential operator.
b)What is the 101st derivative of sinx? That is find g(101).
I have no idea where to start or how to do a). But I think once I have a) it might be easier to understand and work out b). But I thought I would still ask both. Thank you for your assistance in advance.
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
Let's look at sin(x) first.
y=sin(x)
y'(x)=cos(x)
y''(x)=-sin(x)
y'''(x)=-cos(x)
y''''(x)=sin(x), so at the 4th derivative, we're back to sin(x)
n=1,5,9,13,..., derivative=cos(x)
n=2,6,10,14,..., derivative=-sin(x)
n=3,7,11,15,..., derivative=-cos(x)
n=4,8,12,16,..., derivative=sin(x)
g(101) = cos(x)

RELATED QUESTIONS
Let f(x) = sin(ax + b) and let g(x)=cos(a+b) where a and b are constants. Guess a... (answered by greenestamps)

Let f(x) = sin (ax+b) and let g(x) =cos(ax+b) where a and b are constants. Gues a... (answered by solver91311)

I have a test this Thursday and I dont understand this review question at all. Can... (answered by jsmallt9)

Let g(x)n = x(3x-9)^3, find... (answered by Boreal)

please help! I have been looking at this question for just over a week and ive put it off (answered by alka001)

Can someone help me? A sequence {g n} is defined recursively as g 1=72, g n=-2/3*g n-1 , (answered by KMST)

Given g(x)= print_ coeff(m,1)x print_const(b), find g (print_coeff(n,1)a) Please help... (answered by stanbon)

Consider g(x) = x^n + 4x^n - 1; what is the maximum number of turns it can have? @ The... (answered by edjones)

Suppose f is a polynomial function of degree Six such that f(n) =1/n for n=1,2,3,4,5,6,7. (answered by josgarithmetic)