course Mth 164
ah9836@email.vccs.edu
Theta is the reference-circle angle. t is the variable that determines the reference-circle angle, but t is not itself an angle.
The given solution starts with the following two lines:
sin(t+pi/3) = .5 means that sin(theta) = .5, with theta = t + pi/3.
The reference-circle picture of sin(theta) = .5 is given in Figure 60. We see that this occurs at the angle arcsin(.5) = pi/6 as well as at 5 pi/6.
Once you understand these statements the rest follows fairly easily. Can you tell me specifically what you do and do not understand about these statements?
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What I don't understand is where would t be on the coordinate plane ? For example, why is the graph of -3sin(2x+pi/2) not the same as y=-3sin(2t+pi/2) and why is it different ? What is your point of reference for t, specifically for this graph, and in general ?
The graph of y=-3sin(2t+pi/2) vs. t would be identical to the graph of y=-3sin(2x+pi/2) vs. x, which in turn would be identical to the graph of y=-3sin(2u+pi/2) vs. u, or for that matter q=-3sin(2p+pi/2) vs. p.
The symbols used for the variables don't affect the graph.