How do we know that -1 <= sinx <= 1? I dont know how we came to this conslusion

Question

How do we know that -1 <= sinx <= 1? I dont know how we came to this conslusion or how i would find this in other problems like this. Thank you!

Chapter 8.1, Problem 59AYU Bookmark Show all steps: NC ON find the inverse function f-1 of each function f. Find the range of f and the domain and range of f-1 f(x) = 5 sin x + 2; Step-by-step solution Step 1 of 1 Here we need to find the inverse function f of each function f and also to find the range of f and the domain and range of f As for each value of domain of function that is the set of all values of x, f(x) has a unique value thus the function f is one to one and as each element of its range is a pre-image of its domain so f has an inverse function. To find the steps we proceed as under y-5sin+2 Interchange x and y Proceed to solve for y x_2=5siny Sin y Apply the definition of inverse function The inverse function of f is f-(x)-sin i To find the range off, we solve y = 5 sinx + 2 for sinx and use the fact that -1 sin x 1 in x -5S y-2s5 On multiplying all sides by 5 Continue the above steps, we have

Explanation / Answer

Minimum value of sin x is -1 . For any value of x, the value of sin x should never be less than -1. Similarly , maximum value of sin x =1 .

In math form, it can be written as -1<=sin x<=1 .

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