Question

simplify cos 0/ tan 0 cot0

Answer 1

the options are
a)Sin Theta
B)Cos Theta
c)Csc Theta
D)Sec Theta

Pleaseeee help me :(

Answer 2

give it a try its simple...

Answer 3

I did, I have to have a whole semester worth the online schooling done by today or I don't graduate. I need all the help I can get right now.. lol

Answer 4

Hey @tayvaught14

So, to solve this question, you need to have an understanding of Trigonometric Identities.
This is what the question asks.

\[\frac{cos ~\theta}{tan~\theta . cot~\theta}\]

Now what we know is: \[tan ~\theta = \frac{1}{cot~\theta}\]
So, you can write, tan \(\theta\) as that and then see what you get! :D

Try now. :)

Answer 5

Okay hold on, thank you :)

Answer 6

Wait so do I put the fraction for tan theta in the other fraction? I'm sorry I'm very confused on all of this.

Answer 7

No problem! I'll help.

These are some trigonometric Identities:

\[\sin \theta = \frac{1}{csc \theta}\]\[cos \theta = \frac{1}{sec\theta}\]\[tan\theta = \frac{1}{\cot\theta}\]

Are you familiar with these?

Answer 8

Sort of yes

Answer 9

Do you know what trigonometric identities represent?
They are simple ratios of a right angled triangle:



Let's move on to the more lovable part of trigonometry.
Simplification of ratios.

In your question, this is what you are asked to find: \[\frac{cos\theta}{tan\theta.cot\theta}\]

Try to use the IDENTITIES/ THE RELATIONS BETWEEN THE RECIPROCALS. HERE.

Ask if you don't get it. I'll help. But just try once. :D

Answer 10

Okay, Thank you so much! I will ask you when I think I've figured it out :)

Answer 11

Is there an equation or something that would help me figure out what goes where. I understand what you sent me, in a sense, but is there a certain way I plug it into the original problem?

Answer 12

Yes. Totally! :D

This is what you are given: \[\frac{cos\theta}{tan\theta.cot\theta}\]
What do you know about \(tan\theta\) from the identities? :D
We know that: \[tan\theta = \frac{1}{cot\theta}\]
Let us substitute this, in place of \(tan\theta\) in the original equation!
We get:\[\frac{cos\theta}{\frac{1}{cot\theta}.cot\theta}\]

Okay, we have something now! :D

Let's see the denominator.
We have \[\cot\theta.\frac{1}{cot\theta}\] which is equal to ?

Well, it is equal to 1 ! :D
It's just like:
\[2 * \frac{1}{2} = 1 = a * \frac{1}{a} = (anything) * \frac{1}{(anything)} = 1\]

So we now have our denominator = 1.
Numerator still is \(cos\theta\)

Thus the fraction now is = \[\frac{cos\theta}{1} = cos\theta\]

Getting this? If not, Ask, I'll explain. :)

Answer 13

so you substitute the fraction for tan in, and then you multiply it by the denominator to get rid of the fraction?

Answer 14

Yes, I multiply cot [which was already in the denominator before] and then when I multiply it, I get 1. :)

Answer 15

I think I understand that! Would you help me with another now that I sort of get the basics?

Answer 16

Sure. Try it yourself once. Use the above identities.
Go through this link: http://www.mathsisfun.com/algebra/trigonometric-identities.html

I'll be around.

Answer 17

So that page is very helpful thank you! But would you be able to help me get started on this question and I'll finish it? Thank you so much for helping @AkashdeepDeb

Answer 18

I already posted the answer.
Check it again! ^^

Answer 19

You don't understand how much you're helping me right now! lol thank you @AkashdeepDeb

Answer 20

Glad. :)