Duane said:How do you graph f'(x) when f(x)= sin(x+sin2x), 0≤x≤∏ ?
If I calculate f'(x) first by the chain rule, I get f'(x)=cos(x+sin2x)(1+cos2x), where to proceed ?
Thanks for any help in advance.
The graph of a trigonometric function is a visual representation of a mathematical function that involves one or more of the six basic trigonometric functions: sine, cosine, tangent, cotangent, secant, and cosecant. These functions represent the relationship between the angles of a triangle and the side lengths of that triangle.
To plot a graph of a trigonometric function, you need to first choose a specific function (such as sine or cosine) and a specific range of values for the independent variable (usually an angle measure in radians or degrees). Then, use a graphing calculator or software to calculate the corresponding values for the dependent variable (usually the y-coordinate). Finally, plot these points on a coordinate plane and connect them to create the graph.
Some key features of a graph of a trigonometric function include amplitude, period, and phase shift. The amplitude is the maximum distance the graph extends from the midline, the period is the distance between two consecutive peaks or troughs, and the phase shift is the horizontal translation of the graph. These features can be identified by analyzing the equation of the function.
Changing the coefficients in a trigonometric function can affect its graph in different ways. For example, changing the amplitude will change the height of the peaks and troughs, while changing the period will affect the length of the cycle. Additionally, changing the phase shift will shift the entire graph horizontally. Understanding how these coefficients impact the graph can help in analyzing and graphing trigonometric functions.
The unit circle is a fundamental tool for understanding trigonometric functions. The coordinates of points on the unit circle correspond to the values of the sine and cosine functions at different angles. In fact, the unit circle can be used to derive the graphs of all six basic trigonometric functions. Additionally, the unit circle can help in visualizing and understanding the key features of a graph of a trigonometric function, such as amplitude and period.