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# unit circle! Watch

1. 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...
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...
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.
3. (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...
Because and . This is dues to the SOH-CAH-TOA rule.
4. (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.
Because and . This is dues to the SOH-CAH-TOA rule.
Yes I understand that but that doesn't help.
6. (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
7. (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
8. (Original post by SophieL1996)
sorry that does not help, but I have read elsewhere an have figured it out
Are you OK with this now?
9. (Original post by davros)
Are you OK with this now?
Yes with that 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 ??
10. (Original post by SophieL1996)
Yes with that 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)

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