Video Transcript
Is the following statement possible or impossible? csc π equals negative 2.4.
First of all, letβs recall what we mean by csc π. csc π is one over sin π. So what weβre actually asking is, can one over sin of π be equal to negative 2.4? Well, to answer this, weβll consider the domain and range of the function sin of π. The domain is the input to the function, while π can take all real values. So the domain is all real numbers. But what about the range? Well, the range tells us the output of the function.
We know that sin of π oscillates between negative one and one inclusive. Its maximum is one and its minimum is negative one. It wonβt take any values outside of this. So its range is the close interval from negative one to one. We can alternatively write this as sin π is greater than or equal to negative one and less than or equal to one. So, what value of sin π gives us one over sin π equals negative 2.4? Letβs make sin π the subject by multiplying both sides by sin π.
When we do, we get one equals negative 2.4 sin of π. Next, weβre going to divide through by negative 2.4. So sin π is negative one over 2.4 or sin of π is negative five twelfths. Well, we can see that negative five twelfths is indeed greater than or equal to negative one and less than or equal to one. So, sin π can be equal to negative five twelfths, meaning one over sin π can be equal to negative 2.4. Since csc π is the same as one over sin π, we can say that yes, it is possible. csc π can be equal to negative 2.4.