Analyzing the Domain and Range of the Function $f(x) = \frac{1}{1 - \sin x}$
What is the domain and range of the function $f$ defined by $f(x)=\frac{1}{1-\sin x}$?
In my book the solution is the following:
But I have some questions:
1. The domain if $f$ is $\mathbb{R}$-$D$. The elements of $\mathbb{R}$ are real numbers, but the elements of the set $D$ are angles in radians. How is possible the domain is difference of two different sets? (If we want to find the largest domain, we can consider;for example, the set $A$ (whose elements are all the angles in radians) instead of $\mathbb{R}$, this makes more sense!).
2. For its range, I know it is using the following fact: $-1\leq \sin x\leq1$ $\forall x\in \mathbb{R}$. The above I know is true when $x$ is radians or degree. But how is possible that is right for real number? Actually, my question is the following: How to define senx and cosx for x real number in such a way that they continue to fulfill the known properties when x is radian o degree?
- accepted
- 1273 views
- $20.00
Related Questions
- Find the volume of the solid obtained by rotating $y=x^2$ about y-axis, between $x=1$ and $x=2$, using the shell method.
- Find equation of the tangent line using implicit differentiation
- Compute the curl of $F=(x^2-\sin (xy), z-cox(y), e^{xy} )$
- Calculate the following, if it exists: $\int_{0}^{1} x^a(lnx)^mdx$ , where $a > -1$ and $m$ is a nonnegative integer.
- Function Invertibility/Inverse & Calculus, One question. Early Uni/College level
- Characterizing the Tangent and Normal Bundles - Submanifolds in Banach Spaces and Their Classifications
- Accumulation points question (Real Analysis)
- Riemann Sums for computing $\int_0^3 x^3 dx$
