Question

range of function cos(sinx)

Answer 1

Answer on Question # 41274– Math - Functional Analysis

Question:

Find range of function $\cos(\sin x)$

Solution:

Range of $y(x) = \sin(x)$ is $\{y \in R : -1 \leq y \leq 1\}$. So, to find range of $z(x) = \cos(\sin x)$, we should find a range of $z(y) = \cos(y)$ with domain $\{y \in R : -1 \leq y \leq 1\}$. And it is easily seen that the range of this function is $\{z \in R : \cos(1) \leq z \leq 1\}$

Answer: $\{z \in \mathbb{R} : \cos(1) \leq z \leq 1\}$

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