Pre Calc Problem. Think you can do it?

S

Stéphanie

New member
okay so this is a question i saw in my book and its been bugging me because I can't figure it out

Explain why the graphs y= csc x and y= -k sin x will never intersect for any positive value of k

so I set them equal to each other csc x= -k sin x, then I got 1/sin x= -k sin x

which gave me k=1/sin^2x, the graph of this has only a negative range, but I don't know how to explain it
 
I'll try to make this simple

the graph of csc goes along with the sin graph. The graph of csc starts at the maximum and minimum of the sin graph... if you put a negative amplitude on sin, the sin graph will start out going down from 0 and having a minimum at every pi/2 instead of a maximum at every pi/2... the csc graph remains unchanged and will still be where the original sin graph would've been.

So basically the sin graph with the -k will have a minimum where the regular sin graph would normally have had a maximum (which is where the csc graph in the problem is) and that is why they will never intersect.
 
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