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# sin and cos relationship watch

1. okay so i've been taught:

sin(a)=cos(90-a)
cos(a)=sin(90-a)

and i see why this works by working through the graph transformations

but why isn't it shown as:

sin(a)=cos(a-90)
cos(a)=sin(a+90)

assuming that this is right of course

i think that this is a simpler algebraic representation of their relationship because there is only one transformation
2. There are many transformations which will lead to the same result.
In fact, infinitely many.
You can get sin by translating cos by 90, 90 + 180, 90 + 2*180, 90 + 3*180, ... degrees.
Or doing the 90 minus (reflection in the y-axis and translation).
Or combinations of the two.
3. Draw a right angled triangle

Label one angle a and the other one 90-a

Look at the sin and cos
4. (Original post by placenta medicae talpae)
There are many transformations which will lead to the same result.
In fact, infinitely many.
You can get sin by translating cos by 90, 90 + 180, 90 + 2*180, 90 + 3*180, ... degrees.
Or doing the 90 minus (reflection in the y-axis and translation).
Or combinations of the two.

(Original post by TenOfThem)
Draw a right angled triangle

Label one angle a and the other one 90-a

Look at the sin and cos
cheeeeeers

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