circle and you’ll understand why. Sine and cosine have the same values, but they occur at different places on the circle. Features of the Sine and Cosine Curves (page 2) f(x) = sin x f(x) = cos x The sine curve starts at ( 0 , ____ ) and has The cosine curve starts at (0, _____ ), has x-intercepts at x at x = ____ , _____ , _____ , 3π, 4π, =_____ and _____ , has maximum points at ( ____, 1) and etc. This is because of the unit circle. The ( ____, 1), and a minimum point at ( ____ , −1). repeat every ____ units because that is how far apart the points are that have an x-value of As with the sine function, the cosine curve continues on in zero. Remember, the sine function is repetitive or each direction, so the x-intercepts will continue to repeat periodic because the coordinates start to repeat themselves at intervals. Cosine is periodic, as well, π every 2π revolutions around the unit circle. because the angle continues to rotate around the unit circle and the points begin to repeat after one revolution. It has a maximum point at _____ , and a minimum point at ____. Take a look at both of these functions on the same graph. What are the key differences between the two?
circle and you’ll understand why. Sine and cosine have the same values, but they occur at different places on the circle. Features of the Sine and Cosine Curves (page 2) f(x) = sin x f(x) = cos x The sine curve starts at ( 0 , ____ ) and has at x = ____ , _____ , _____ , 3π, 4π, etc. This is because of the unit circle. The repeat every ____ units because that is how far apart the points are that have an x-value of zero. Remember, the sine function is repetitive or periodic because the coordinates start to repeat every 2π revolutions around the unit circle. It has a maximum point at _____ , and a minimum point at ____. The cosine curve starts at (0, _____ ), has x-intercepts at x =_____ and _____ , has maximum points at ( ____, 1) and ( ____, 1), and a minimum point at ( ____ , −1). As with the sine function, the cosine curve continues on in each direction, so the x-intercepts will continue to repeat themselves at π intervals. Cosine is periodic, as well, because the angle continues to rotate around the unit circle and the points begin to repeat after one revolution. Take a look at both of these functions on the same graph. What are the key differences between the two?
1004NotetakingGuideAlgebraIIv14.docx