A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 one year ago
I'm really struggling with establishing identities and I would seriously love some help.
Here are two questions I need answered:
https://i.imgur.com/BnFBQ33.png
and
https://i.imgur.com/nK2VeCH.png
I'm not sure where to start with either of these, and I really would like to know how to solve them and what the answers are. Any advice would be helpful!
Thanks in advance!! :)
anonymous
 one year ago
I'm really struggling with establishing identities and I would seriously love some help. Here are two questions I need answered: https://i.imgur.com/BnFBQ33.png and https://i.imgur.com/nK2VeCH.png I'm not sure where to start with either of these, and I really would like to know how to solve them and what the answers are. Any advice would be helpful! Thanks in advance!! :)

This Question is Closed

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0does it help to know that \[\tan(\theta)=\frac{\sin(\theta)}{\cos(\theta)}\]?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Yes! I found a sheet of a few things like that but I'm not exactly sure how they work. http://tutorial.math.lamar.edu/pdf/Trig_Cheat_Sheet.pdf

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so for the first one \[\cos(\theta)\tan(\theta)=\cos(\theta)\frac{\sin(\theta)}{\cos(\theta)}=\sin(\theta)\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0it is mostly algebra the cosines cancel

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1They have the answer choices written out in one long line, which makes it a bit tricky to sort things out. I find it better to have it written out like this \[\Large \cos(\theta)\tan(\theta) = \sin(\theta)\] \[\Large \cos(\theta){\color{red}{\tan(\theta)}} = \sin(\theta)\] \[\Large \cos(\theta){\color{red}{\frac{\sin(\theta)}{\cos(\theta)}}} = \sin(\theta)\] At this point, I'm sure you see what cancels. Throughout the whole process, the right side stays the same.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0the second one is completely different it is derived from the "subtraction angle" formula \[\sin(\alpha\beta)=\sin(\alpha)\cos(\beta)\cos(\alpha)\sin(\beta)\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0put \(\alpha=\frac{\pi}{2}\) and \(\beta=\theta\) and you get it

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Okay, I think I get the canceling thing. One the first one at least. for the first question would the answer would be B since the \[\cos()\] cancel out and \[\tan( \theta)\] equals sin over cos, which equals the others. Is this correct?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Sorry for the weirdness, I'm not super sure how to use the equation button. I meant: \[\cos (\theta)\]

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1yes the first one is B

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I'm still a little stuck with the second question. Would it be C since the subtraction angle formula comes out to be sin(π/2−θ)=sin(π2)cos(θ)−cos(π/2)sin(θ) which matches the first part of the equation? Some of this stuff is going over my head.

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1You have it correct.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Thanks both of you! :3

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1you're welcome
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.