Afunction f(x) is even if f(−x) = f(x). which of sine or cosine is even? explain how you know. (b) a function f(x) is odd if f(−x) = −f(x). which of sine or cosine is odd? explain how you know. (c) cosine is a shift of sine. that is, cos(x) = sin(x + c) for some value of c. (actually this is true for many many values of c.) find such a value of c and explain how you know that you are correct.

a. Cosine is an even function

b. Sine is an odd function

c. cos(x) = sin(x + pi/2)

Step-by-step explanation:

See the plot attached.

a. In the figure it can be seen that, for example, cos(pi/2) = cos(-pi/2); therefore, cosine is even.

b. In the figure it can be seen that, for example, sin(pi/2) = 1;  sin(-pi/2) = -1; therefore, sine is odd.

c. Function displacements along x-axis are made adding (or subtracting) values to x; i. e., f(x + a), where a is a constant, displace the function f(x) a steps to the left. It can be seen in the figure that sine is cosine but displaced pi/2 values to the right. So, sin(x + pi/2) will displace sine pi/2 values to the left, where cosine is placed.

i think there was a typo. you wrote pat brings 3 quarts of ice-cream to the party. each serving of ice-cream is 1 6 quart. how many total servings of ice-cream does pat bring to the party? i think the bold is supposed to be 1/6. so 1 quart of ice cream = 6 servings. 6 * 3 = 18.