split-solution of equation with tan and cot

[Zeezrom]

This seems like it should be simple. However I have a critical lack of trigonometry knowledge.

The problem is...
tan-cot=0


I need measures of degrees from this. There are 4 solutions in all.

Thanks Everyone!

 

[Deleted member 4993]

This seems like it should be simple. However I have a critical lack of trigonometry knowledge.

The problem is...
tan-cot=0


I need measures of degrees from this. There are 4 solutions in all.

Thanks Everyone!

use tan (x) = cot(?/2 - x)

\(\displaystyle tan(\theta) - cot(\theta) = 0\)

\(\displaystyle tan(\theta) = cot(\theta)\)

\(\displaystyle tan(\theta) = tan(\frac{\pi}{2} - \theta)\)

Now continue.....

 

[Zeezrom]

I'm seeing one solution as 90 degrees. Is that correct?

Thanks for all the help BTW.

 

[Deleted member 4993]

I'm seeing one solution as 90 degrees. Is that correct?

Thanks for all the help BTW.

How did you get that?

tan(?/2) = undefined

cot(?/2) = 0

Those are not equal.

 

[mmm4444bot]

ANOTHER WAY.

I have a critical lack of trigonometry knowledge.

I can show you how to change the equation

tan(x) - cot(x) = 0

into the equation

sin(x) = ± ?2/2

What is the significance of the latter equation?

If you don't know, then your lack is critical. Too critical even to be attempting work with tangents and cotangents.

Are you in a math course? Self-studying?

Good grief! How many times am I going to edit this post?

 

[Mrspi]

This seems like it should be simple. However I have a critical lack of trigonometry knowledge.

The problem is...
tan-cot=0


I need measures of degrees from this. There are 4 solutions in all.

Thanks Everyone!

If tan theta - cot theta = 0, then

tan theta = cot theta

You did not state whether there are any limits on the domain of theta....

I suggest that you look at the unit circle...you should have a unit-circle diagram in your text. If you don't, you can surely find MANY by doing an Internet search on Google or your favorite search engine.

The unit-circle diagram should show you where tan theta = cot theta

You say you should have FOUR solutions....I don't see that, unless there are domain restrictions which are not stated.

Tan theta = cot theta in quadrant I, and tan theta = cot theta in quadrant III. Were you given some restrictions on theta?

 

[Zeezrom]

Re: ANOTHER WAY.


I can show you how to change the equation

tan(x) - cot(x) = 0

into the equation

sin(x) = ± ?2/2

What is the significance of the latter equation?

If you don't know, then your lack is critical. Too critical even to be attempting work with tangents and cotangents.

Are you in a math course? Self-studying?

Good grief! How many times am I going to edit this post?[/quote]


Deriving sin from this equation does ring a bell.

a possible solution 49.39? If that's wrong please bear with me

Yes I'm self studying, and understand up until the point of knowing which quadrant a certain angle falls in.

Could anyone tell me what concepts, tables, etc. I Need to know to continue successfully in trigonometry.

I thank you all for your patience!

 

[Zeezrom]

This seems like it should be simple. However I have a critical lack of trigonometry knowledge.

The problem is...
tan-cot=0


I need measures of degrees from this. There are 4 solutions in all.

Thanks Everyone!

If tan theta - cot theta = 0, then

tan theta = cot theta

You did not state whether there are any limits on the domain of theta....

I suggest that you look at the unit circle...you should have a unit-circle diagram in your text. If you don't, you can surely find MANY by doing an Internet search on Google or your favorite search engine.

The unit-circle diagram should show you where tan theta = cot theta

You say you should have FOUR solutions....I don't see that, unless there are domain restrictions which are not stated.

Tan theta = cot theta in quadrant I, and tan theta = cot theta in quadrant III. Were you given some restrictions on theta?

Sorry, the domain is 0<x<360 It's the less than or equal to sign, but I can't figure out how to express that on my keyboard.

Thanks!

 

[mmm4444bot]

a possible solution 49.39? This is not correct.

Could anyone tell me what concepts, tables, etc. I Need to know to continue successfully in trigonometry.

You need to understand the rules of algebra, to be able to correctly manipulate trigonometric equations.

You need to memorize some basics (eg: sine and cosine values for all of the special angles, definitions of tangent, cotangent, secant and cosecant in terms of sine and cosine, the unit circle, the concept of reference angles, understanding how the quadrant in which the terminal ray of the angle lies affects the signs of the trigonometric values for that angle).

A working knowledge of basic geometry, so that you can sketch diagrams and "see" relationships.

What types of materials and resources are you using to self-study? Do you have a textbook?

We have the following definitions for tangent and cotangent, in terms of sine and cosine.

tan(x) = sin(x)/cos(x)

cot(x) = cos(x)/sin(x)

So, we can write the following for tan(x) = cot(x).

sin(x)/cos(x) = cos(x)/sin(x)

It seems intuitive that this equation is true whenever sin(x) = cos(x) because that makes the proportion 1 = 1.

The first angle from 0 degrees through 360 degrees where sine equals cosine is 45 degrees. This reference angle, along with our knowledge of the signs of sine and cosine in Quadrant I and Quadrant III (or, our knowledge of the unit circle) tells us that 225 degrees also satisfies the given equation.

And, if we realize (perhaps, algebraically) that -sin(x)/cos(x) also equals cos(x)/-sin(x), then the angle in Quad II and the angle in Quad IV which both have a reference angle of 45 degrees will enter our mind as solutions, too.

But, we should not rely on intuition alone. We can solve the proportion above to show that it is true whenever sine equals ±?2/2. That happens (from 0 degrees through 360 degrees) only at the four angles whose reference angle is 45 degrees.

Cheers ~ Mark

 

[mmm4444bot]

the domain is 0<x<360 It's the less than or equal to sign, but I can't figure out how to express that on my keyboard.

If you're using Microsoft Windows, you can copy a bunch of symbols from the Character Map applet. (Look for it in either the "Accessories" or "System Tools" submenu).

Let me know, if you need help figuring out how to type these "extra" characters using Windows.

? ? ? ? ? ? ? ± ? ? × Ø ß ÷ ? ? ? ?

 

[soroban]

Hello, Zeezrom!

\(\displaystyle \text{On the interval }[0^o,\:360^o] \text{, there are 4 solutions.}\)

Solve: .\(\displaystyle \tan\theta - \cot\theta \:=\:0\)

\(\displaystyle \text{We have: }\:\tan\theta \,=\,\cot\theta \quad\Rightarrow\quad \tan\theta \,=\,\frac{1}{\tan\theta} \quad\Rightarrow\quad \tan^2\!\theta \,=\,1\)


\(\displaystyle \text{Hence: }\:\tan\theta \,=\,\pm1 \quad\Rightarrow\quad \theta \:=\:45^o,\;135^o,\;225^o,\;315^o\)

 

[Zeezrom]

Thank You ALL so much!

You have helped me more than you know. I think I'll get better at this now.