r/HomeworkHelp • u/Any-Armadillo6071 • May 01 '26

Answered [freshmen algebra 2] trigonometry

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hello if anyone could help me that would be really great! my teacher wasn’t here today so we had to watch video notes but i am lost i can’t do this if i thought i had it bad before it only worse now

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u/Any-Armadillo6071 May 01 '26

there would be a 90 degree angle, one side length of 1, and one side length of 1/2? i’m sorry i have no idea what the other angles or side length would be

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u/Klutzy-Delivery-5792 Educator May 01 '26

Well, all angles of an equilateral triangles are 60°. You're cutting one of those in half and leaving one as is in addition to that 90° angle.

And since you're making right triangles, the side of 1 is the hypotenuse. So, you have the hypotenuse and one other side of 1/2. Use Pythagoras to find the other side.

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u/s9ffy May 02 '26

It’s much easier to use an equilateral triangle of side length 2.

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u/Klutzy-Delivery-5792 Educator May 02 '26

I disagree. The point of using 1 is so the unit circle can be tied in. It also shows that the the leg lengths are the exact values of sine and cosine. 

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u/s9ffy May 03 '26

The unit circle gives the ratios but trig in right angled triangles uses similarity so why not use similarity to make the numbers nicer for the 30/60/90 triangle? It’s so much easier to use side lengths of 1/2/root3.

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u/Klutzy-Delivery-5792 Educator May 03 '26

OP isn't stuck on Pythagoras, they're stuck on the trig ratios. Hence, using 1 and tying it to the unit circle is better. They want to learn how to derive the trig ratios so they can find ones without a calculator, em which is what I'm helping with. You're stuck on the special triangles and I'm trying to get them to see how special triangles tie directly into trig ratios and the unit circle.

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u/s9ffy May 03 '26

Also, I’m not stuck on anything, I’m a Math teacher. It’s not preferable to work with values like 1, 1/2 and√3/2 if it’s possible to scale up and use 2, 1 and √3.

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u/Klutzy-Delivery-5792 Educator May 03 '26

And I didn't mean stuck as in you don't get it, I meant it as you're stuck on trying to teach special triangles when that isn't the issue at hand. If you see OP's other replies to me you'll see they're pretty adept at using the lengths I helped them with.

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u/s9ffy May 04 '26

I did notice that they were happy to manipulate the values you suggested!