#how can 130* have a sine

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next coralBOT
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inland swift
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when ur first introduced to trig, you deal with triangles

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the formal definition after that is using a unit circle

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trigonometry can deal with any positive or negative angle

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if u look at the unit circle u can see that sine is defined for any and all angles

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the triangle is the most basic definition and is not the formal definition for trig

coarse wedge
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But isn’t sine for example the ratio between opposite and hypotenuse?

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How could a 130* triangle have them

void kestrel
void kestrel
coarse wedge
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Wait so is sine always just the y value?

void kestrel
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yea it’s the y value of a unit circle

coarse wedge
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And that’s by definition

void kestrel
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yup

coarse wedge
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Oh ok that makes sense

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So it’s like any other function

inland swift
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we need a unit circle to use them as a function

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a triangle cant do that

coarse wedge
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Ok so the application for trig from what I can see went from tryna figure triangle lengths

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To figuring out locations relative to each other

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Is that correct?

inland swift
coarse wedge
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So you know how trig ratios only worked with figuring out distances between a triangle but with trig functions what you are dealing with is location or distance for all angles. So let’s say we have a motor that turns a arm 240 degrees anticlockwise then the location would be at ((rcos(240),(rsin(240). Where r is the length of the arm

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So it’s just a way to measure distance given a angle and one length

inland swift
inland swift
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and its still valid for finding lengths of triangles

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best of both worlds