A community for students.
Here's the question you clicked on:
 0 viewing
cassieforlife5
 one year ago
Find period, domain, and range of y= 3 csc (3x + pi) 2
y=3 csc 3 (x+ pi/3) 2 but I'm stuck from here.
This is review from last year, but I've totally forgotten everything about trig functions. Not looking for just answers but also explanations!
cassieforlife5
 one year ago
Find period, domain, and range of y= 3 csc (3x + pi) 2 y=3 csc 3 (x+ pi/3) 2 but I'm stuck from here. This is review from last year, but I've totally forgotten everything about trig functions. Not looking for just answers but also explanations!

This Question is Open

freckles
 one year ago
Best ResponseYou've already chosen the best response.2The period of y=csc(x) is 2pi. So the period of y=csc(bx) is 2pi/b.  y=sin(x) on [2pi,2pi] looks like: dw:1440611891389:dw We can see the period is 2pi. The reciprocal function of y=sin(x) is y=csc(x). So noticed the zeros of y=sin(x) on [2pi,2pi], they were at x=2pi,pi,0,pi,2pi y=csc(x) will be undefined there. Notice where sin(x)=1 on [2pi,2pi], they were at x=3pi/2,x=pi/2 well this is where csc(x)=1 also since the reciprocal of 1 is still 1. Notice where sin(x)=1 on [2pi,2pi], they were at x=pi/2,3pi/2 well this where csc(x)=1 since the reciprocal of 1 is still 1. The graph of y=csc(x) looks like: dw:1440612297776:dw you can also from this graph that the range is (inf,1] union [1,inf) and the domain is everything but where we had the zeros fro sin(x) which was npi where n is integer  Anyways...we have \[\csc(x) \le 1 \text{ or } \csc(x) \ge 1 \text{ from the range } \\ \text{ this holds for any input } \\ \csc(3x+\pi) \le 1 \text{ or } \csc(3x+\pi) \ge 1 \\ \text{ multiply both sides by 3 and then subtract both sides by 2 } \\ \text{ \to find range of } y=3\csc(3x+\pi)2\]  Now for the domain part... You could solve the following equation to find out what numbers to exclude: \[\sin(3x+\pi)=0\]

cassieforlife5
 one year ago
Best ResponseYou've already chosen the best response.0Thank you for the awesome details! I'm still a bit confused but I'll try and go over it a few times. Could you help with the equation for finding the domain as well?
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.