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unit circle!

I understand the unit circle, however how do you know that sin90=1 and cos(-90)=0 I don't quite understand how that works... :smile:
Reply 1
Original post by SophieL1996
I understand the unit circle, however how do you know that sin90=1 and cos(-90)=0 I don't quite understand how that works... :smile:


I'm not sure I understand the question. The unit circle is a method for demonstrating sines and cosines parametrically as x2 + y2 = 1
x = cos(t) and y = sin(t)
Looking at the circle at certain x and y coordinates you can see that this is true.
Reply 2
Original post by SophieL1996
I understand the unit circle, however how do you know that sin90=1 and cos(-90)=0 I don't quite understand how that works... :smile:


Because sinθ=OHsin\theta=\frac{O}{H} and cosθ=AHcos\theta=\frac{A}{H}. This is dues to the SOH-CAH-TOA rule.
Reply 3
Original post by joostan
I'm not sure I understand the question. The unit circle is a method for demonstrating sines and cosines parametrically as x2 + y2 = 1
x = cos(t) and y = sin(t)
Looking at the circle at certain x and y coordinates you can see that this is true.


in the book it says sin90=1 because p has coordinates (0,r) so sine =r/r. How do you know that P has those coordinates sine I do not know what sine 90 looks like on the unit circle.
Reply 4
Original post by Asklepios
Because sinθ=OHsin\theta=\frac{O}{H} and cosθ=AHcos\theta=\frac{A}{H}. This is dues to the SOH-CAH-TOA rule.


Yes I understand that but that doesn't help.
Reply 5
Original post by SophieL1996
in the book it says sin90=1 because p has coordinates (0,r) so sine =r/r. How do you know that P has those coordinates sine I do not know what sine 90 looks like on the unit circle.


Read the above post. The hypotenuse = 1. The sides are x and y
Reply 6
Original post by joostan
Read the above post. The hypotenuse = 1. The sides are x and y


sorry that does not help, but I have read elsewhere an have figured it out :smile:
Reply 7
Original post by SophieL1996
sorry that does not help, but I have read elsewhere an have figured it out :smile:


Are you OK with this now?
Reply 8
Original post by davros
Are you OK with this now?


Yes with that :smile: but just one question, it says given that theta is an angle measured in degrees, express in terms of sine theta: sin(-360+theta) I understand how to work this out, but I thought the answer was -sine theta rather than +sine theta ??
Reply 9
Original post by SophieL1996
Yes with that :smile: but just one question, it says given that theta is an angle measured in degrees, express in terms of sine theta: sin(-360+theta) I understand how to work this out, but I thought the answer was -sine theta rather than +sine theta ??


No, imagine going round the unit circle - it doesn't matter whether you go round +360 degrees (anticlockwise) or -360 degrees (clockwise), you just get back to where you started from, so your x- and y-coordinates are the same as they were originally.

so sin(-360 + theta) = sin theta = sin(+360 + theta)
and
cos(-360 + theta) = cos theta = cos(+360 + theta)

:smile:

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