Define sine and cosine for every angle with the unit circle. Find their signs, values and periods, and draw the graphs of all six functions, with their stretches and shifts.
3 lessons, about 1 h 25 min3 simulations11 problems5 practice questionsPython in every lesson
Created by StemPy LabPut a point on a circle of radius and turn it through an angle . Its coordinates are . This defines sine and cosine for every real number . It also gives the identity and leads to tan, cot, sec and cosec.
The quadrant of decides the signs of the six functions. The values at , , , and give the value at every multiple of these angles, once whole turns are taken away. Sine and cosine repeat every , and tan and cot every . The domain and range of each function follow from the circle.
Unrolling the unit circle gives the wave of . The graph of is the same wave moved to the left. has period and breaks at the odd multiples of . The graph of has amplitude and period . It is moved sideways by and up by .
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