The figure above shows the graph of 2sin 4 y x π = + , 0 2≤ ≤x π. The graph meets the y axis at the point A and the point C is one of the two x intercepts of the curve. The point B is the maximum point of the curve. a) State the coordinates of A, B and C. The straight line with equation y = − 3 meets the graph of 2sin 4 y x π = +

Trigonometric Graphs Summary Functions One Cycle of the Graph Domain Range Amplitude Period all real numbers 1 all real numbers 1 all real numbers except where is an integer all real numbers none −3 all real numbers except where is an integer all real numbers none all real numbers except

Recalling Section1.7, we see from this formula that the graph of y= sin(x) is the result of shifting the graph of y= cos(x) to the right ˇ 2 units. A visual inspection con rms this. Now that we know the basic shapes of the graphs of y = cos(x) and y = sin(x), we can use Theorem1.7in Section1.7to graph more complicated curves.

Sep 18, 2017 · Graph of the Sine Function To sketch the graph of y = sin x first locate the key points. These are the maximum points, the minimum points, and the intercepts. sin x 0 1 0 -1 0 x 0 2 π 2 3π π 2π Then, connect the points on the graph with a smooth curve that extends in both directions beyond the five points. A single cycle is called a period ...

• Graph trigonometric functions. • Find the amplitude and period of variation of the sine, cosine, and tangent functions. Translations of Trigonometric Graphs(pp. 769–776) optional 2 optional 1 • Graph horizontal translations of trigonometric graphs and find phase shifts. • Graph vertical translations of trigonometric graphs.