Some different trig representations with Y13, which we could then combine to derive the compound angle formulae. I think the multipliers were a new way of thinking for a lot of them, but they work really well here and will be useful in mechanics! #MathsToday #ALevelMaths - ThreadSky

catrionaagg.bsky.social • 171 days ago

Some different trig representations with Y13, which we could then combine to derive the compound angle formulae. I think the multipliers were a new way of thinking for a lot of them, but they work really well here and will be useful in mechanics! #MathsToday #ALevelMaths

1 / 2

Comments

drbennison.bsky.social•170 days ago

Love the multipliers being shown on the diagram :) that’s a really neat way of doing it.

mrcfmaths.bsky.social•170 days ago

Snap! I used a rectangle with the triangles in. @tlmaths.bsky.social special.

jamiewoodmaths.bsky.social•171 days ago

I've never thought about actively teaching that idea of multipliers; I like that a lot!

catrionaagg.bsky.social•171 days ago

We’ve started doing this lower down the school as our main method. Students often find it easier to find the hypotenuse, especially if they’re not great at rearranging equations.

paddymacmahon.com•171 days ago

Us too, and only tan to begin with. Tan is the scale factor you multiply the adjacent by to make the opposite. The reverse problem is then easy. And we actively compare with using scale factors for percentage change.

tombutton.bsky.social•171 days ago

It still baffles me why we teach so many relationships as quotients and not products!

opp=hyp×sin θ is easier to understand and use.

davegjones.bsky.social•171 days ago

Does it make the trig functions more 'magic' and less maths to students? Does it lead to less teaching of what sin(x) is as a function? It also doesn't fit as well with the special triangles for exact values, IMO.

catrionaagg.bsky.social•170 days ago

My gut feeling is “no” to the first two questions, so I’d be interested to hear why you think it does.

segarrogers.bsky.social•170 days ago

As for the ‘special’ triangles, well, they’re specific to trig-as-ratios … the ‘special’ triangles for trig-as-lengths are different!

catrionaagg.bsky.social•170 days ago

What’s would your versions of special triangles look like?

segarrogers.bsky.social•170 days ago

If you start trig from a similar triangles perspective (with sin, cos, tan as lengths) then the multipliers are just a nice procedural framework that sits on top of the maths.

davegjones.bsky.social•170 days ago

I do start with unit hyp and sin as the height, cos as the base, but then we evolve to ratios as they are more general and the trig functions are what we are defining.

tombutton.bsky.social•170 days ago

It's more of a change of perspective so that ratios are seen as multipliers generally:

sin: what you mulitply the hypotenuse by to get the opposite
speed: what you multiply time by to get the distance
gradient: what you multiply change in x by to get change in y

davegjones.bsky.social•170 days ago

This is a lot to think about (and quick answers are rarely my best answers). I am concerned about rates down the road, dy/dx as a multiplier feels worrying. I think trig is different to the others because it is a function of the angle.

nicole-cozens.bsky.social•171 days ago

Exactly- and this is so evident from using the unit circle

jwrightmaths.bsky.social•171 days ago

My biggest bug bear like this is cosine rule being the wrong way round.

a² + b² - 2abCosC = c² relates so much nicer to Pythag, and can easily explain that the extra cluster is compensation for the angle.

But it will never change in formula sheets

miss-agd.bsky.social•170 days ago

The more people that make this point, the more likely it'll get heard!

ridermeister.bsky.social•171 days ago

Why not? Let's start a movement! I like to think of the extra term as the deficit (which turns into a surplus when the relevant angle is obtuse).

jwrightmaths.bsky.social•170 days ago

Yeah the reason I go for compensation is that I spend ages talking about proportion between side and angle, so we already go into big with big, small with small. Deficit and surplus definitely a good way to go though!

It's like how tau will never replace pi...pure apathy by the laymen 😂

paddymacmahon.com•171 days ago

I used a similar idea to your diagram for the rsin(θ+α) form:

https://www.desmos.com/calculator/uucrc4h31j

@desmos.bsky.social

Comments

Posting Rules

Reply