Trigonometry

This goes for all math really. Just because your job doesn't require math doesn't mean others don't. Just think of all the things made by engineers. Cars, planes, washing machines, phones and so many more. These were all made by using math. If math were never here then we would be living in a completely different world.

Are there any good resources to explain Unit circles, quadrantal angles, complementary angles, and rotational vs reference trigonometric ratios? I've been struggling the most with this unit and I don't really know how to tackle this. I don't want to fail :(

Thanks in advance!

I’ve worked my ass off this semester to understand trig and get good grades. So far we have taken 3 exams and I got over 95 on all of them.

However, this feels so weird to me because I don’t consider myself the brightest math student and it takes me a few hours to complete an exam while using my notes and reference book. Learning from home is so different.

In a classroom setting I feel like there is no way I’d pass the exams with an A considering we are usually given 2 hours to complete a test and sometimes can’t use notes.

With that being said I have an A but don’t feel like an A student. Am I wrong to feel this way?

I've been out of school for quite a while, so perhaps some things have changed. My understanding is that most high school curriculums cover algebra, geometry, trigonometry, and for advanced students, pre-calculus or calculus. I'm not aware of a national standard that requires statistics.

For most people, algebra - geometry - trigonometry are rarely if ever used after they leave school. I believe that most students don't even see how they might use these skills, and often mock their value.

Basic statistics can be used almost immediately and would help most students understand their world far better than the A-G-T skills. Simply knowing concepts like Standard Deviation can help most people intuitively understand the odds that something will happen. Just the rule of thumb that the range defined by average minus one standard deviation to the average plus one standard deviation tends to cover 2/3's of the occurrences for normally distributed sets is far more valuable than memorizing SOH-CAH-TOA.

I want to know if there are good reasons for the A-G-T method that make it superior to a focus on basic statistics. Help me change my view.

Edit:

First off, thank everyone for bringing up lots of great points. It seems that the primary thinking is falling into three categories:

A. This is a good path for STEM majors - I agree, though I don't think a STEM path is the most common for most students. I'm not saying that the A-G-T path should be eliminated, but that the default should replace stats for trig.

B. You cannot learn statistics before you learn advanced math. I'm not sure I understand this one well enough as I didn't see a lot of examples that support this assertion.

C. Education isn't about teaching useful skills, but about teaching students how to think. - I don't disagree, but I also don't think I understand how trig fulfills that goal better than stats.

This isn't a complete list, but it does seem to contain the most common points. I'm still trying to get through all of the comments (as of now 343 in two hours), so if your main point isn't included, please be patient, I'm drinking from a fire hose on this one ¯\_(ツ)_/¯

Edit #2 with Analysis and Deltas:

First off, thank everyone for your great responses and thoughtful comments!

I read every topline comment - though by the time I got to the end there were 12 more, so I'm sure by the time I write this there will still be some I didn't get to read. The responses tended to fall into six general categ

Title. If there is will there be calculus involved in them? Or what is expected of you to know? Thanks..

Title. Austerity measures have meant the public high school I teach at has had to squeeze these two classes into one, and they’re making me teach it? I’m a math graduate, I am really not prepared to self-learn Archaeology before September. Any advice?

I just want to talk

"From the window of his hotel in (information that doesn't matter), Max can see statues of (a bunch of stuff that doesn't matter). The angle formed by Max's lines of sight to the top and to the foot of the statue of Chief Whitecap is 3 degrees. The angle of depression of Max's line of sight to the top of the statue is 21 degrees. The horizontal distance between Max and the front of the statue is 66 metres.

Determine the height of the statue and the line-of-sight distance from where Max is standing at the window to the foot of the statue."

I'm finding the actual solving pretty straightforward, but how the heck do I figure out how to draw the diagram?? Is there any way to do so, because I'm struggling so much with these stupid word problems. Thanks!

Korang ingat tak hampir pecah otak, sakit kepala ke nak belajar semua perkara tu.

Itu belum gauge, EMF (electromotive force) ada juga yang terkonfius dengan electromagnetic field, EMP (yang ni boleh merosakkan semua peralatan dan gadget electronik sebab ada pulse ). Siapa tahu remote sensing (digunakan masa pencarian MH370 dulu). Aku cakap tentang remote sensing lah. Dulu masa kat kuliah, lecturer asyik discuss pasal nanotechnology. Sekarang aku rasa dah ada pico technology.

Korang boleh recognize East dan West dengan senang tak masa belajar Geografi dulu? Sebab cara differentiate yang mana satu Timur dan yang mana satu Barat ialah dengan berapa ratus kali entah aku kena lukis peta Australia dulu. Cikgu aku asyik-asyik ulang chapter Australia, dia suka sangat dengan peta Australia. Habis tu aku dengan student lain asyik lukis peta Australia yang paling banyak. Kan Australia ada West Australia. Aku tahu direction West tu, tahulah arah bertentangan dengannya ialah East 😆 .

Ada lagi banyak perkara yang aku tahu tetapi seperti wise words atau kata-kata bijaksana ini...

"All the knowledge in the world is like a drop of water in a vast ocean."

That 'vast ocean' are all the knowledge unknown to human race.

Ilmu pengetahuan yang diketahui manusia hanyalah sekadar setitis air yang jatuh ke dalam lautan yang luas.

Masih terlalu banyak yang tidak kita ketahui.

Dan jika kamu hanya menuntut ilmu akademik kalau tidak disusuli dengan akhlak, moral dan common sense, kamu masih manusia yang tidak berguna di atas muka bumi. Dengan hanya menuntut ilmu akademik saja tapi common sense was not built-in inside you, berkemungkinan besar kamu hanya akan membawa kemusnahan dan kebinasaaan kepada umat manusia.

If you think that you're smart enough, read this sci-fi story written by Isaac Asimov. It's one of the many stories in Asimov's fiction about robots or he mostly called them humanoid , a shortform for human android. There's a short story about how a group of brilliant scientists sent a robot into the future and after the robot comes back to their present, they asked the humanoid what the robot saw in the future. The robot described everything he saw in the future. But the fatal mistake made by the brilliant human scientists is they forgot or they do not ask one important/crucial question to the robot (humanoid). What was the question which they do not ask ❓⁉️

So, given this function:

f(x) = sin(x+pi/4) + cos(x-(pi/4))

I am meant to find the amplitude, period, and phase/vertical(?) shift, compared to a sinus curve that intersects the origin.

I gathered that: https://media.discordapp.net/attachments/269573202018041856/839081224534229002/821005187836805152.png?width=2160&height=366

And then: https://media.discordapp.net/attachments/269573202018041856/839082102674292747/821005187836805152.png?width=2160&height=300

At this point, I am lost in what I should do. Someone mentioned a ”trigonometric R method,” or ”auxillary angle method.” Additionally, they mentioned the ”phasor diagram.” I have no idea what any of this is. I am a trigonometry beginner, and I am still rusty with my trigonometric identities.

They said that the idea is to multiply 1/(sqrt(a^2+b^2)) to asinx+bcosx to relate it with the identity sin(A+B). What?

Explain like I'm 5, thanks.

Hey! I was wondering if anybody knew of any chips that perform basic trigonometry functions? or other math functions? I'm looking to create some synth modules, and have been very inspired by Instruo's tanh(3) module, which calculates the inverse tan of an incoming audio signal. If anyone knows of a chip that I could send control voltage through and get the sin/cos/log of it out of!

Let me know if anyone knows of any chips that could do something like that. Or if there's a chip that might be different but have related/similar capabilities that I should check out! Thanks in advance :)

1. I need help with this solution. Can someone explain why cos 18 in the denominator can't be rewritten as sin (90-18)? Another part of the solution. I am supposed to show that cos 54° / cos 18° = 2 sin 18°. I was thinking cos 54° / cos 18° => sin (90-54) / sin (90-18) => sin 36 / sin 72. I was thinking that sin(36) / sin(2*36) => sin 36 cancel each other out.
2. What formula do we use when finding out what sin 15° cos 15° is? The question is here, iirc the first identity can be rewritten as sin(x)cos(x)=sin(2x)/2. Done properly, how do we end up with 1/2 sin 30° from this? 1/2 * 2 is 1, so we end up with sin 15° cos 15°. How do they get 1/2 sin 30°?
3. I also need help understanding this. Why did they convert cos 312° to cos(-312°)? And how did we go from cos(-312°) to cos(360°-312°)?
4. Then we have this bullshit. Why did they go from sin 204° and cos 204° to sin(180°+24°)/cos(180°+24°)? And why does that lead us to having = -sin24°/-cos24° = (a/sqrt (1-a^2))
5. But wait, there's more. Why is sin(-132°) = -sin(180°-132°) exactly? Why does that equal -sin48°?

I've been having trouble with my last homework question on my Trigonometry class. Here's the question:

What is the radian measure of the smaller central angle made by the hands of a clock at 8:00?

Please need some help.

1. Simplify
   a) (sin x + cos x)2 - sin 2x
   b) sin 4x / sin 2x
2. Calculate exactly for sin v/2 = 2/5, where v is an acute angle
   a) cos v/2
   b) sin v
3. Determine without a calculator sin v * cos v if cos 2v = sqrt (8) / 3, 0°≤v≤90°

1.The solution online for the first question, a), says that (sin x + cos x)2 - sin 2x = sin2x + 2sinx * cos x + cos2x - sin2x, and I just want to know where the heck they pulled this from? Note that I don't understand b) either.

2. The solution for this question says that for a), the pythagorean identity gives us cos2 v/2 = 1 - sin2 v/2. How? For b), it says ”the formula for the double angle gives us sin v = 2 * sin (v/2) * cos (v/2). Sin v = 2*2/5*√(21)/(5) = 4√(21)/25. How?

3. The solution states that ”the pythagorean identity gives us sin2 2v = 1 - cos2 2v = 1 - (√8/3)2 = 1 - 8/9 = 1/9, sin 2v = √(1/9) = 1/3.

Because 0°≤v≤90° then it holds that 0°≤2v≤180° and therefore sin 2v>0. sin 2v = 2 sin v * cos v = 1/3 => sin v * cos v = 1/6.

Someone please explain everything step by step because I'm super dumb.

A man is standing 35 m from a government building. On top of the building is a Canadian flag. From the man, the angle of elevation of the top of the building is π/6 radians and the angle of elevation of the top of the flag is π/3 radians. Determine an exact expression for the distance from the top of the flag to the top of the building.

thank you for any place to get started :)

A tree standing vertically on level ground casts a 110 foot long shadow. The angle of elevation from the end of the shadow to the top of the tree is 23 degrees. Find the height of the tree rounded to 1 dec.

I tried solving this problem using 110sin(23), and I got 42.980, rounded to 43.

The actual answer is 46.7, but I can’t figure out how to get that.

I checked and my calculator is in degrees as it should be (not radian).

Any tips for solving this?

Edit: I was confused by the angle of elevation so I put the 23 degrees in the wrong spot. Your replies were very helpful. Thank you!

Is it permissible to write the solution like this, if not, why?

Context: I am meant to simplify sin(pi/6) * cos(3pi/4) - cos^2 (pi).

I was taught that it becomes easier if the angle is 45° or 60° when working with sine or cosine.

I'm in high school and would like a very complete book to self-study

But if it’s not asking too much, preferably a book that is captivating to read

Looking for a college student or a tutor who’s good at math to help me take my Trigonometry test on mymathlabs that is due by 11:59pm tmrw. The test is 30 questions. I don’t have much money but will pay with what I can. Any help would be much appreciated

The way I'm thinking about it is that 3pi is 1.5 revolutions of the unit circle, which puts you at (-1,0). From there tangent is 0/-1. Doesn't that mean arctan should be -1/0, making it undefined? Thank you.

help