Can You Simplify the Trigonometric Expression (sin120+tan120) / (sin150+tan150)?

[brandon26]

(sin120+tan120) / (sin150+tan150)
I tried to simplify this, but it only gets more complicated. I converted the sin120 to sin 60, the sin150 to sin30. How can I make the tan 120 simpler, the rule sinQ/cosQ=tanQ is not useful because you end up with an angle for cos which is greater than 90 and cannot get any simpler. PLease help!

 

[Dr.Brain]

Above expression reduces to:

$<br /> \frac{cos30 - cot30}{cos60-cot60}$

Put the values for all , the answer you get is:

$\frac{3}{2- \sqrt3 }$

 

[brandon26]

How did you do that?

 

[OlderDan]

How did you do that?

Why would you want to? There are endless ways to rewrite the original expression. If all you are going to do is evaluate it, why bother changing it? It was no easier to evaluate in the second form than it was in the first.

 

[brandon26]

I still don't understand how to simplify it?

 

[Dr.Brain]

do you know the values for cos30, cos 60 ,cot 60 ,cot30?

Or are you confused at how you should change sin(90+30) to cos30?

 

[brandon26]

yes, I am confused how to change sin to cos. Also, how did you change tan, and what is cot?

 

[Dr.Brain]

Refer to your basic mathematics book.You need to revise your basic and practise problems.refer to your teacher.

 

[brandon26]

listen you stupid monkey. I came here because I am at home and I need to sort out this problem now. ok forget, your are a useless moron.

 

[brandon26]

if i was able to refer to my teacher, I would not be hear, such a prick you are.

 

[brandon26]

I asked you to help me go through the solution, not just give it to me. You need some serius help

 

[Dr.Brain]

These are the basics of trigonometry.Click the link below to have a look at basics.

http://www.acts.tinet.ie/trigonometry_645.html


Please don't bounce at someone, referring to the textbook and then look at the problem.

cot and tan are the basics of trignometry, so I thought you might need to retreat the basics.

 

[brandon26]

These are the basics of trigonometry.Click the link below to have a look at basics.

http://www.acts.tinet.ie/trigonometry_645.html


Please don't bounce at someone, referring to the textbook and then look at the problem.

cot and tan are the basics of trignometry, so I thought you might need to retreat the basics.

I know all about the basics. All i want to know is how to solve the problem. I know that sin30=1/2, I know that sin^2Q+cos^2Q=1, just please show me how to solve the problem.

 

[OlderDan]

I know all about the basics. All i want to know is how to solve the problem. I know that sin30=1/2, I know that sin^2Q+cos^2Q=1, just please show me how to solve the problem.

You need to let us know the conditions imposed on you for finding the solution. Using my calculator, I can simply evaluate the expression you posted and come up with an answer accurate to several decimal places. In trigonometry, problems are often stated in a manner that excludes decimal answers. The phrase "exact value" is the usual clue that such a solution is required.

"Simplify" means to find an equivalent expression involving fewer terms than the original expression. It does not mean to evaluate the expression. It seems to me that what you are in fact trying to accomplish here is an exact evaluation of the expression. This is not a problem about simplifying at all. It is an evaluation problem. I could be wrong, but based on the prior comments that's how it sounds to me.

The facts you need to know to evaluate this expression are the values of sines and cosines for the special angles where they can be expressed exactly. You have stated one of them: sin 30 = 1/2. That, combined with properties of the sine and cosine, including the identity you stated (Pythagorean indentity), is all you need to evaluate the expression.

From your first post I will assume that all you are stuck on is the evaluation of cos 120 and cos 150. What you need to know about the cosine is the basic property that for any angle A

cos(A) = cos(-A) = -cos (180 - A) = -cos (180 + A) = cos(360 - A)

which can be verified from the graph of the cosine function or by comparison of the trigonometric ratios of angles in standard position in the x-y plane.