What can you say about the graph of y=sin(t) at these values of ?

Question

Abigail Armstrong · Accepted Answer

See the graph, for the t-intercepts, #t = kpi, k = 0, +-1, +-2, +-3, ...#.

combined graph with t-intercepts for y = tan t and the wavy y = sin t #t = kpi#, k = 0, +_1, +-2, +-3, ...# graph{x-pi+0y)(x+pi+0y)(x-2pi+0y)(x+2pi+0y)=0}

Abigail Armstrong · Answer

undefined The graph of $ y = \sin(t) $ represents a sine function, which is a periodic function that oscillates between -1 and 1. As $ t $ varies, the graph of $ y = \sin(t) $ repeats its pattern indefinitely. At $ t = 0 $, the value of $ \sin(t) $ is 0. As $ t $ increases, $ \sin(t) $ increases to a maximum value of 1 at $ t = \frac{\pi}{2} $, then decreases back to 0 at $ t = \pi $, continues to decrease to a minimum value of -1 at $ t = \frac{3\pi}{2} $, and returns to 0 at $ t = 2\pi $. This pattern repeats for all integer multiples of $ 2\pi $.