Simplifying Trigonometric Identities

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In summary, the conversation discusses the value of tan(theta) and various hints are given to solve the problem. The original question is from an entrance exam and the participants debate on the most efficient way to solve it. Some suggest using trigonometric identities while others propose a simpler mathematical rearrangement method. The conversation also touches on the importance of understanding and intuition in problem-solving.
  • #1
yaseen shah
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tan.jpg


in above image what is value of tan[theta].
a)y/y+2x b)x/x+y c)y/y+x d)y/x

This is not Home work! this question belongs to entry test.Which I
can not solve so please do not give hints.
 
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  • #2


This looks like homework.

What do you think? The primary purpose of this site is to help students do their homework. We do not do it for you. Please show some work.
 
  • #3


Hint:
What is [tex]tan(x+\pi/4)[/tex]
 
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  • #4


Gerenuk said:
Hint:
What is [tex]tan(x+\pi/4)[/tex]

What sort of hint is that?
 
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  • #5


SonyAD said:
What sort of hint is that?
This forum is not for lazy students who don't want to do their homework and we are not supposed to do it for them. So I gave a hint only. With that hint you can solve the problem without any thought about geometry. It's a 4 line mathematical rearrangement.
 
  • #6


SonyAD said:
What sort of hint is that?
It's and excellent one! I will admit that for a moment I forgot that the smaller right triangle had both legs of length x:blushing:.
 
  • #7


Gerenek, from your hint, I found the answer using the formula for tan(α+β). Is this an acceptable way to go about it? It took me than four steps...
 
  • #8


My solution was both general and intuitive. It helps in understanding how & why. The insight gained will be useful in the real world.

The proverbial fishing pole.
HallsofIvy said:
It's and excellent one! I will admit that for a moment I forgot that the smaller right triangle had both legs of length x:blushing:.

The solution based on the little triangle being isosceles won't work if it isn't.
 
  • #9


SonyAD said:
My solution was both general and intuitive. It helps in understanding how & why. The insight gained will be useful in the real world.
There is nothing intuitive about the need for new sketches and a length derivation. Also you fail the exam by running out of time if you solve the tasks much more generally than needed.
 
  • #10


SonyAD said:
My solution was both general and intuitive. It helps in understanding how & why. The insight gained will be useful in the real world.

The proverbial fishing pole.
What solution? Your entire contribution to this thread was "What sort of hint is that?"


The solution based on the little triangle being isosceles won't work if it isn't.
In this problem it is. Gerunuk gave a hint to solve this problem.
 
  • #11


It got deleted in exchange for an infraction.
 
  • #12


yaseen shah said:
This is not Home work! this question belongs to entry test.Which I can not solve so please do not give hints.
Hints are all you'll get here, I'm afraid. If this question is from an entrance exam, and a student doesn't know how to do problems like these, then he/she shouldn't belong to the program/school/course he/she is entering? :confused:

Gerenuk's hint is excellent. Do you know your trigonometric identities?

Gerenuk said:
With that hint you can solve the problem without any thought about geometry. It's a 4 line mathematical rearrangement.
It took me 6 lines, not 4, but I tend to write more steps than probably what is necessary. :blushing:69
 

FAQ: Simplifying Trigonometric Identities

What is the definition of tangent?

The tangent of an angle is the ratio of the length of the opposite side to the length of the adjacent side in a right triangle.

How do you find the value of tan[theta]?

The value of tan[theta] can be found by using a scientific calculator or by using the trigonometric function tables.

What is the range of values for tan[theta]?

The range of values for tan[theta] is from negative infinity to positive infinity, as it is a continuous function.

Can the value of tan[theta] be negative?

Yes, the value of tan[theta] can be negative depending on the value of the angle theta. For example, if theta is in the second or fourth quadrant, the tangent will be negative.

How is tan[theta] used in real-life applications?

Tan[theta] is used in various fields such as engineering, astronomy, and geography to calculate distances, heights, and angles. It is also used in navigation and surveying to determine the direction and location of objects.

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