(4 points) What is the maximum and minimum values of the sine and cosine function? Only consider angles in [0,2𝜋)

Question

Also what angles do they occur at? I can figure out the minimums and maximums but I am not sure how to find which angles they are at.

Answer 1

maximum values of sines and cosines are positive 1

minimum values are negative one

at angle = 0, cosine is at a maximum = 1

at angle = pi/2 the sine is at its maximum = 1

at pi, cosine is at a minimum = -1

at 3pi/2, sine is at a minimum = -1

draw a unit circle and some right triangles and look at the opposite side over the hypotenuse and the adjacent side over the hypotenuse, that's the sine and cosine. the right triangle collapses into a vertical line at 90 and 270 degrees and collapses into a horizontal line at 0 and 180 degrees. those are the angles of maximum and minimum values for sine an cosine: 0, pi/2, pi and 3pi/2 or 0, 90, 180, and 270 degrees.

or you could just graph the sine an cosine functions. at 0 degrees cosine is at its max = 1, follow the curves and they alternate between a max of 1 and a min of -1 with a period of 2pi