Expert: Sherman D. - 6/2/2008

Question
Hey Sherman --

My math instructor for trigonometry has tried time and time again to teach me how to read a sine/cosine graph and be able to tell which is sine, and which is cosine. When the max/min is NOT at the origin, how do I know if it's sine, or just translated cosine? I have been trying for hours to figure this out, and just can't seem to get it! Can you please help me out here?? Thanks!

-- Riley

Answer
there's not to much of a difference between the 2.

sin(x) = cos(x - (pi/2))
cos(x) = sin(x + (pi/2))

cos(A) = x/r
sin(A) = y/r

cos(A) is negative at Quadrants II and III
cos(A) is positive at Quadrants I and IV
sin(A) is positive at Quadrants I and II
sin(A) is negative at Quadrants III and IV

the only real way to tell the difference is to plug in values and see which works.

sin(A) = 0, if A = 180 or 0
cos(A) = 0, if A = 90 or 270

if you go to http://www.calculator.com/calcs/GCalc.html

you can get a graph of your trig problems.