What is 1 - sin(x) equal to?
Understand the Problem
The question is asking for the value of the expression 1 - sin(x), which is a basic trigonometric identity. The goal is to understand or simplify this expression in the context of trigonometric functions.
Answer
The value of the expression $1 - \sin(x)$ ranges from $0$ to $2$, inclusive.
Answer for screen readers
The value of the expression $1 - \sin(x)$ ranges from $0$ to $2$, inclusive.
Steps to Solve
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Identify what the expression is about
The expression we are working with is $1 - \sin(x)$. This term involves the sine function, which is a fundamental trigonometric function. -
Consider the range of the sine function
The sine function, $\sin(x)$, has a range of values from $-1$ to $1$. Therefore, $1 - \sin(x)$ will vary based on the value of $\sin(x)$. -
Analyze maximum and minimum values
To find the minimum value of the expression $1 - \sin(x)$, we consider the maximum value of $\sin(x)$, which is $1$.
$$ 1 - \sin(x) \geq 1 - 1 = 0 $$
To find the maximum value of the expression, we look at the minimum value of $\sin(x)$, which is $-1$.
$$ 1 - \sin(x) \leq 1 - (-1) = 2 $$
- Determine the final range of the expression
Thus, the expression $1 - \sin(x)$ can vary from $0$ to $2$. Therefore, we can conclude that: $$ 0 \leq 1 - \sin(x) \leq 2 $$
The value of the expression $1 - \sin(x)$ ranges from $0$ to $2$, inclusive.
More Information
This expression demonstrates the basic behavior of the sine function in the context of trigonometry. It shows how the sine function can shift values when subtracted from a constant.
Tips
- Forgetting the range of the sine function can lead to miscalculating the range of the expression.
- Not considering all possible values of $x$ which can lead to overlooking the maximum and minimum values of the expression.
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