Question

can someone help me with sine and cosine?... please?

Answer 1

yep, tell me, what do you need to know?

Answer 2

okay i need help to describe properties of the graph of the Cosine Function, f(theta) = cos(theta) or the graph of the Sine Function, f(theta) = sin(theta) and relate the property to the unit circle definition of either function because i have no clue what to do :/

Answer 3

so you need to understand what the unit circle is and how sine and cosine work

Answer 4

see, I'll draw it

Answer 5

naw i need to understand how to find Amplitude, Period, Domain, Range, and x-intercepts c: because i already get the unit circle

Answer 6

its simply understanding what these two websites are saying http://www.afralisp.net/archive/lisp/bulge.htm and https://www.khanacademy.org/math/trigonometry/unit-circle-trig-func/Trig-unit-circle/v/unit-circle-definition-of-trig-functions-1
and i do understand that, its just i dont quite understand how to find the properties of them

Answer 7

when you relate the unit circle to the graph of the sine you are talking about the angle, when the angle is 0 and 180, the sine is 0 because the line of the unit circle is horizontal, while the cosine is 1 (with 0) or -1 (with 180) for the same reason, on the other hand, the cosine is 0 when the angle is 90 and 270 because the line is comletely vertical, ans so the sine is 1 (at 90º) or -1 (at 270º)

Answer 8

the amplitude is exacty that value, and it corresponds to the height of the line (in the case of the sine) or the length of the line (in the case of the cosine)

Answer 9

here you can see that at 45º they intersect, because the value is the same in that case, its a right triangle so it follows the pythagorean theorem and they both have the same length
\[\frac{ \sqrt{2} }{ 2 }\]
for both sine and cosine \[(\frac{ \sqrt{2} }{ 2 })^2+(\frac{ \sqrt{2} }{ 2 })^2=c=\frac{ 2 }{ 4 }+\frac{ 2 }{ 4 }=1\]