The derivatives of repeat every four orders

MATHEMATICS · Subjective · CBSE · Mathematics · Continuity and Differentiability · Continuity and Differentiability

Problem

The derivatives of

h(x)=\sin x

repeat every four orders. Identify the remainder

r\in\{0,1,2,3\}

such that

h^{(n)}(x)=-\cos x

when

n\equiv r\pmod 4

, and briefly explain the pattern that justifies your answer.