I hate trig..

[SparklyUnicorn]

I don't know what it is, but I have a mental block whenever I see anything with trig.  I know my skills in that area are weak, but damn I have been working at it for awhile.  I mostly fake and memorize my way through those questions.

 

Thank goodness we are allowed a sheet of notes for exams.  It would not be pretty otherwise. 

 

Any suggestions?  Like is there a book "Trig for the Complete Moron"?  LOL

 

 

[regentrude]

What about trig are you struggling with? memorizing trig identities? Or basic SOHCAHTOA?

 

[Barb_]

Just a commiseration. I hate trig too. I love math but I really hate trig. One of my older kids took math through Calc III, linear algebra and differential equations as electives just for fun. But she hates trig.

 

Then there is another daughter who LOVED trig even though she never thought math was her thing. Trig is math weird the way chemistry is science weird. People either love it or hate it, it seems. I hated Chem too even though I loved bio and physics.

 

Sorry just chatting. No real suggestions. Listen to Regentrude

[regentrude]

If it's trig identities, remember that you can derive them all very quickly when you use the trig functions in their exponential form with e^+/-i theta. So no need to stress about obscure identities.

If its about the behavior of the functions, visualizing what happens to the sides of a right triangle when the angle is varied helps a lot.

Edited September 29, 2017 by regentrude

[Arcadia]

Gelfand’s trigonometry book PDF http://users.auth.gr/~siskakis/GelfandSaul-Trigonometry.pdf

 

See if it helps explains better.

 

ETA:

What topic are you stuck on?

Edited September 29, 2017 by Arcadia

[Guest]

Unit circle is your friend

[Caroline]

There is a Cliff Notes trig book. Pretty basic and helpful.

[SparklyUnicorn]

If it's trig identities, remember that you can derive them all very quickly when you use the trig functions in their exponential form with e^+/-i theta. So no need to stress about obscure identities.

If its about the behavior of the functions, visualizing what happens to the sides of a right triangle when the angle is varied helps a lot.

 

Yeah and I have to admit I don't find this quick nor do I understand it.  LOL

 

I asked my kid to explain a few things and that helped.

[JanetC]

We used Trigonometry Success in 20 minutes a Day.

 

It's out of print, but Amazon has a few copies and google found a PDF.

[Caroline]

Yeah and I have to admit I don't find this quick nor do I understand it. LOL

 

I asked my kid to explain a few things and that helped.

You aren't alone. A lot of people don't make this connection.

[EKS]

I hate trig too.  I can do it, but it isn't at all intuitive.  

[SparklyUnicorn]

I hate trig too.  I can do it, but it isn't at all intuitive.  

 

That is just it.  It is not intuitive to me. 

[regentrude]

That is just it.  It is not intuitive to me. 

 

Again, I am asking: WHAT specifically about trig is the issue? Depending on that, I can make suggestions.

[Caroline]

You can PM me if you want. I teach trig from right triangle trig in geometry all the way through using it in multivariable calculus. I'd be glad to help in any way I can.

[daijobu]

When I look back at my old high school trig exams, I find unit circles drawn EVERYWHERE, in the margins, here and there.  They look like little planets orbiting my test papers.  Then I have little lines drawn to pi/3 or 5*pi/6 to remind me what the angles are.  

 

The only thing you should have to memorize is SOHCAHTOA, which is just the definition of sine, cosine, and tangent.  Everything else is Pythagorean theorem, basically.  And if you forget, draw the unit circles and the right triangles created.  It helps to be able to rattle off the sines of pi/4 and pi/6, etc., but really if you ever forget, you should be able to re-derive it on the spot by drawing a right triangle.  Do you know your 30-60-90 and 45-45 right triangles?  That should help a lot.  

 

Or are you having trouble with graphing the sine curves or the tangent curves?  That's a matter of plugging in various values of x and seeing what happens to the y-value.  If you do it enough, it should come quickly.  If you know that the sin0 = 0, and the period is 2*pi, you can start there and just draw it.   But it also helps to plot in the intermediate points to get a more accurate curve.  (I would get points taken off if my curves were too "pointy.")

[SparklyUnicorn]

Again, I am asking: WHAT specifically about trig is the issue? Depending on that, I can make suggestions.

 

Ok, an example

 

evaluate the integral:

 

sinx

--------            dx

cosx +cos^2x

 

(had to fudge that a bit)

 

So I got to the point of:

 

LN absolute value of cosx +1 over cosx +C

That is the answer before the final answer (the prof would be fine with my answer). The book says LN absolute value of 1+sec x + C.  Why?  I don't know how to get to that point.  No clue.  Whatever I'd need to know to get to that point...I just don't know. 

[SparklyUnicorn]

When I look back at my old high school trig exams, I find unit circles drawn EVERYWHERE, in the margins, here and there.  They look like little planets orbiting my test papers.  Then I have little lines drawn to pi/3 or 5*pi/6 to remind me what the angles are.  

 

The only thing you should have to memorize is SOHCAHTOA, which is just the definition of sine, cosine, and tangent.  Everything else is Pythagorean theorem, basically.  And if you forget, draw the unit circles and the right triangles created.  It helps to be able to rattle off the sines of pi/4 and pi/6, etc., but really if you ever forget, you should be able to re-derive it on the spot by drawing a right triangle.  Do you know your 30-60-90 and 45-45 right triangles?  That should help a lot.  

 

Or are you having trouble with graphing the sine curves or the tangent curves?  That's a matter of plugging in various values of x and seeing what happens to the y-value.  If you do it enough, it should come quickly.  If you know that the sin0 = 0, and the period is 2*pi, you can start there and just draw it.   But it also helps to plot in the intermediate points to get a more accurate curve.  (I would get points taken off if my curves were too "pointy.")

 

I am not confused by the SOHCAHTOA thing.  My kid helped me with graphing and that's getting less fuzzy. 

 

 

[regentrude]

sinx

--------            dx

cosx +cos^2x

 

(had to fudge that a bit)

 

So I got to the point of:

 

LN absolute value of cosx +1 over cosx +C

That is the answer before the final answer (the prof would be fine with my answer). The book says LN absolute value of 1+sec x + C.  Why?  I don't know how to get to that point.  No clue.  Whatever I'd need to know to get to that point...I just don't know. 

 

But that has nothing to do with trig! That is simplifying fractions using basic algebra.

 

I assume you mean  [(cos x+ 1) over cos x] + c., with the integration constant added to the fraction, not to the denominator.

 

(cos x + 1)/ cos x= 1+ 1/cos x   This is just algebra and no strange trig stuff.

 

Knowing that 1/cos x is called sec x you get 1+ sec x + c

Edited October 2, 2017 by regentrude

[SparklyUnicorn]

But that has nothing to do with trig! That is simplifying fractions using basic algebra.

 

I assume you mean  [(cos x+ 1) over cos x] + c., with the integration constant added to the fraction, not to the denominator.

 

(cos x + 1)/ cos x= 1+ 1/cos x   This is just algebra and no strange trig stuff.

 

Knowing that 1/cos x is called sec x you get 1+ sec x + c

 

That's exactly what I don't know. 

[regentrude]

That's exactly what I don't know. 

 

OK, so that's probably because your trig course did not cover secant and cosecant.  These are simply names for the functions 1/cos x and 1/sin x. 

I can tell you that these are not really important. As a physicist, I had to take tons of math and math physics, and never heard of them until recently. 

This does NOT mean you are bad at trig. Just that nobody introduced these names to you.

Edited October 2, 2017 by regentrude

[SparklyUnicorn]

OK, so that's probably because your trig course did not cover secant and cosecant.  These are simply names for the functions 1/cos x and 1/sin x. 

I can tell you that these are not really important. As a physicist, I had to take tons of math and math physics, and never heard of them until recently. 

This does NOT mean you are bad at trig. Just that nobody introduced these names to you.

 

I have heard of them, but obviously either not enough or I forgot the details.  There are so many topics covered in algebra and pre calc that it is hard to know every single one of them inside and out.  In Calc 1 and 2 so far we don't focus on nearly as many topics.  I actually find this sort of less difficult because of that. 

[Arcadia]

I have heard of them, but obviously either not enough or I forgot the details. There are so many topics covered in algebra and pre calc that it is hard to know every single one of them inside and out.

The terms cosecant, secant and cotangent are covered briefly in high school math. Same goes for matrices. You just revise when you need to use it and realized you have forgotten.

My oldest remembers things like double and triple angle formulas but my youngest has to refresh his memory before semester exams and other tests else once he move on to another topic he forgets. My husband has definitely forgotten much of his college math that he doesn’t use for his work.

[daijobu]

This article should help you with learning some of the less common trig functions.  

 

My favorite trig function from the above is

 

heybabywhatsyoursine(theta)=1, if theta=awful pickup line and =0 otherwise

[SparklyUnicorn]

The terms cosecant, secant and cotangent are covered briefly in high school math. Same goes for matrices. You just revise when you need to use it and realized you have forgotten.

My oldest remembers things like double and triple angle formulas but my youngest has to refresh his memory before semester exams and other tests else once he move on to another topic he forgets. My husband has definitely forgotten much of his college math that he doesn’t use for his work.

 

I graduated from high school in 1992 so...

LOL

 

As far as I'm concerned, nothing was covered in high school. 

[kiana]

I have this book and it's a pretty good reference. I lend it to my students who haven't taken math in forever. https://www.amazon.com/Just-Time-Algebra-Trigonometry-Calculus/dp/032167104X

[luuknam]

I agree, trig sucks (and I should probably read a trig book). 

 

The only thing you should have to memorize is SOHCAHTOA, which is just the definition of sine, cosine, and tangent.  Everything else is Pythagorean theorem, basically. 

 

Well, no, since:

 

If it's trig identities, remember that you can derive them all very quickly when you use the trig functions in their exponential form with e^+/-i theta. So no need to stress about obscure identities.

 

 

Imaginary numbers were not covered in high school. Other than the teacher once explaining just for a heck of it they exist (but, that was him going off-topic, and basically only that the square root of negative one is this weird thing people decided to call i (obviously I learned a bit about them after coming to the US, where you're expected to have a clue about them on the SAT, etc)). 

 

Also, I don't think the unit circle helps much with remembering what an arctan is, or sinh, etc. Nor would it give much of a clue as to what the real life reason might be for taking the integral of such things. 

[SparklyUnicorn]

Imaginary numbers were covered when I was in high school.  I also did cover them in college algebra/trig.  The bit of trig we did wasn't much.  I did more trig in pre calc, but I guess some stuff I either forgot or it's some sort of gap in my knowledge...or I don't know.