# what is trigonometry?

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#1
can someone break down trigonometry for me please?
0
3 years ago
#2
you already want to know the end of the story?
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3 years ago
#3
Mr - wait not Mr but Sir - so Sir Trigonometry finds its roots in the unit circle. It is the circle of centre (0,0) and radius r=1. A point P on the circle is defined as the cosine (which would be the x-axis) and the sine (the y-axis) of the angle formed between the x-axis and the line OP in a new unit: the radian. We have one full turn of the unit circle being 2pi radians (as perimeter is 2pi r and r is here 1). Each angle of Ox with OP is therefore a fraction of 2pi. More specifically, 90 degrees=pi/2 radians etc...
0
3 years ago
#4
More symbolically,

If the angle formed between Ox and OP is theta, therefore P(cos(theta), sin(theta)).
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#5
(Original post by PMC01234)
Mr - wait not Mr but Sir - so Sir Trigonometry finds its roots in the unit circle. It is the circle of centre (0,0) and radius r=1. A point P on the circle is defined as the cosine (which would be the x-axis) and the sine (the y-axis) of the angle formed between the x-axis and the line OP in a new unit: the radian. We have one full turn of the unit circle being 2pi radians (as perimeter is 2pi r and r is here 1). Each angle of Ox with OP is therefore a fraction of 2pi. More specifically, 90 degrees=pi/2 radians etc...
lol i said break it down not destroy my understanding.
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3 years ago
#6
it's like triangles and angles and stuff
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3 years ago
#7
(Original post by imhannahhhhh)
lol i said break it down not destroy my understanding.
an image would be helpful here:

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3 years ago
#8
^^This image is the best one to explain trig, since this is how it's properly defined.

Broadly speaking it connects distances along circles to distances along straight lines. That is trigonometry. 'Sine' and 'cosine' are just the names we give to the functions that connect these two types of distance.
1
3 years ago
#9
Someone will correct me if I'm wrong, but I believe trigonometry was invented to find the distance to stars moving in the sky in a circular motion. So if you are looking at a star at some angle x, then the height of that star perpendicular to the ground is called sinx and the distance from where you're looking to the perpendicular is called cosx. We can then define the rest of trigonometry from these values.
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3 years ago
#10
(Original post by Desmos)
Someone will correct me if I'm wrong, but I believe trigonometry was invented to find the distance to stars moving in the sky in a circular motion. So if you are looking at a star at some angle x, then the height of that star perpendicular to the ground is called sinx and the distance from where you're looking to the perpendicular is called cosx. We can then define the rest of trigonometry from these values.
Yeah this is correct (provided that the distance between you and the star is 1 unit).
As I've said we're defining functions - sine and cosine - that connect distances along circles - the circle centred at you and radius from you to the star - to distances along straight lines - the ones you described.
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