Dear Maria Manzur,
Your question is: How can I difference trigonometric graphs? I cannot differ which is a tan, cos, or sin graph. Do I have to memorize them?
Remember that a graph is described by its function’s equation. Once you understand the process behind each trigonometric function, you can reproduce their graphs. Make sure not to memorize information that you can deduce from the basic concepts. The graphs of sin(x) and cos(x) are similar. To obtain the cos(x) graph, you must shift the sin(x) graph π/2 units in the negative x direction. To obtain the sin(x) graph, you must shift the cos(x) graph π/2 units in the positive x direction. The easiest way of distinguishing between the sin(x) and cos(x) graphs through observation is by determining their value at the origin. Cos(x) “starts” at 1, but sin(x) “starts” at 0. In other words, cos(0)=1 and sin(0)=0. The graph of tan(x) is quite different. It holds characteristics such as tan(0)=0 and vertical asymptotes at x = π/2 + πn (n any integer). But again, just memorizing this sets you apart from someone who can derive it from more basic knowledge.
Your question is: How can I difference trigonometric graphs? I cannot differ which is a tan, cos, or sin graph. Do I have to memorize them?
Remember that a graph is described by its function’s equation. Once you understand the process behind each trigonometric function, you can reproduce their graphs. Make sure not to memorize information that you can deduce from the basic concepts. The graphs of sin(x) and cos(x) are similar. To obtain the cos(x) graph, you must shift the sin(x) graph π/2 units in the negative x direction. To obtain the sin(x) graph, you must shift the cos(x) graph π/2 units in the positive x direction. The easiest way of distinguishing between the sin(x) and cos(x) graphs through observation is by determining their value at the origin. Cos(x) “starts” at 1, but sin(x) “starts” at 0. In other words, cos(0)=1 and sin(0)=0. The graph of tan(x) is quite different. It holds characteristics such as tan(0)=0 and vertical asymptotes at x = π/2 + πn (n any integer). But again, just memorizing this sets you apart from someone who can derive it from more basic knowledge.
1 comment:
Thanks a lot for answering my question. I did the graphs and definetely noticed the difference.
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