Part V The symmetry of the unit circle is useful is generating the trigonometric values for an infinite number of angles. It is also useful in illustrating whether the sine and cosine functions are even or odd. take 30o as an example. In the picture below = 30o. Fill in the missing t Let’s information. Based on the graphs of sine and cosine that we studied in previously, we know that sine is sine is an odd function and cosine is an even function. What about the graphs help us to know this? The graph of is symmetrical about the origin and the graph of is symmetrical about the How can we use the information in #23 to further show that sine is an odd function and cosine is an even function? Since the x-values of t are the same that means that the cosine values for 30o and -30oare equal which is the definition of an even function: . The values for the sine of 30o and -30oare opposites which is the definition of an odd function: Right Triangles and the Unit Circle:
Part V The symmetry of the unit circle is useful is generating the trigonometric values for an infinite number of angles. It is also useful in illustrating whether the sine and cosine functions are even or odd. Let’s take 30o as an example. In the picture below t = 30o. Fill in the missing information. Based on the graphs of sine and cosine that we studied in previously, we know that sine is sine is an odd function and cosine is an even function. What about the graphs help us to know this? The graph of is symmetrical about the origin and the graph of is symmetrical about the How can we use the information in #23 to further show that sine is an odd function and cosine is an even function? Since the x-values of t are the same that means that the cosine values for 30o and -30oare equal which is the definition of an even function: . The values for the sine of 30o and -30oare opposites which is the definition of an odd function: Right Triangles and the Unit Circle: