sin and cos relationship

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 :tongue:

i think that this is a simpler algebraic representation of their relationship because there is only one transformation

Reply 1

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.
Let your imagination run wild :p:

(edited 11 years ago)

Reply 2

TenOfThem

18

Draw a right angled triangle

Label one angle a and the other one 90-a

Look at the sin and cos

Reply 3

TPJY

OP

10

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.
Let your imagination run wild :p:

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 :smile:

sin and cos relationship

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