Please I am having a hard time understanding their relations
#sine and cosine identities (symmetry)
bitter sierra
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Please I am having a hard time understanding their relations
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bitter sierra
bitter sierra
look here
this is their relations
I do not know how sin(-theta) = - sin(theta)
if cos(theta) = cos(-theta)
timid slate
if cos(theta) = cos(-theta)
What do you mean "if"?
bitter sierra
What do you mean "if"?
no if
timid slate
no if
No, like, it sounds like you think there is some kind of relationship between sine and cosine that makes sin(-x) = -sin(x) and cos(-x) = cos(x) inconsistent.
bitter sierra
oh
bitter sierra
No, like, it sounds like you think there is some kind of relationship between si...
so there is no relationship with cosine and sine?
only cosine and cosine?
timid slate
so there is no relationship with cosine and sine?
There is, but not one that's inconsistent with the given identities.
bitter sierra
so where do we start
timid slate
so where do we start
...start with what?
bitter sierra
understanding
timid slate
understanding
...uh, start by understanding the unit circle definition of the trig functions, because that's what the diagram is using to illustrate its point.
timid slate
can you explain why sin(-theta) = -sin(theta)
...do you understand the unit circle definition of trig functions?
bitter sierra
yes
bitter sierra
when i go counter clockwise the angle is positive
when i go clockwise the angle is negative
timid slate
...how is that a definition of the trig functions?
bitter sierra
x is cosine and y is sine
timid slate
x and y of what?
bitter sierra
axis
timid slate
It's sounding like the answer is no, you don't know the definition.
timid slate
because when apathy teaches me i understand it very well
Okay, so.
We have an angle whose measure is theta.
What we want to do first is replicate this angle in the Cartesian plane in what's called "standard position".
"Standard position" is when one ray of the angle is the positive x-axis, the angle measure of theta is measured counterclockwise, and the vertex of the angle is the origin.
That is, our first ray is the positive x-axis, then our second ray is a copy of the first, rotated counterclockwise about the origin by theta.
The second thing we want to do is draw the unit circle, which is the circle with center (0, 0) and radius 1.
Then we define cos(theta) to be the x-coordinate of the point of intersection between the unit circle and the second ray of the angle with measure theta in standard position.
Similarly, sin(theta) is the y-coordinate of the same point.
bitter sierra
That is, our first ray is the positive x-axis, then our second ray is a copy of ...
what is this
timid slate
what is this
What do you mean, "what is this"?
It's... a description of an angle in standard position.
bitter sierra
What do you mean, "what is this"?
can I see an illustration
timid slate
This is the illustration. The green, blue, yellow, and pink arcs all illustrate angles in standard position.
Notice how all of the arcs originated at the positive x-axis.
bitter sierra
okay
timid slate
...do you get it?
bitter sierra
yes
bitter sierra
Notice how all of the arcs originated at the positive x-axis.
the green, pink and yellow arcs are all going counter clockwise
the blue is the only one going clockwise
is that important too?
timid slate
the blue is the only one going clockwise
A positive rotation clockwise is equivalent to a negative rotation counterclockwise.
Hence the blue angle expressing measure -theta.
timid slate
then we are done?
...are we? You tell me, you're the one who doesn't understand this stuff.
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@bitter sierra