Question

F(x) = sin(x), basis B = {sin(x) + cos(x), cos(x)}, basis C = {cos(x) − sin(x), sin(x) + cos(x)} in span(sin(x), cos(x))

Answer 1

The values of f(x)[B] and f(x)[C] are {sin²(x) + sin(x)cos(x), sin(x)cos(x)} and {sin(x)cos(x) − sin²(x), sin²(x) + sin(x)cos(x)}, respectively

How to evaluate the products?

The trigonometry functions are given as:

f(x) = sin(x)

B = {sin(x) + cos(x), cos(x)}

C = {cos(x) − sin(x), sin(x) + cos(x)}

The product f(x)[B] is:

f(x)[B] = f(x) * B

So, we have:

f(x)[B] = sin(x) * {sin(x) + cos(x), cos(x)}

Evaluate the product

f(x)[B] = {sin²(x) + sin(x)cos(x), sin(x)cos(x)}

The product f(x)[C] is:

f(x)[C] = f(x) * C

So, we have:

f(x)[C] = sin(x) * {cos(x) − sin(x), sin(x) + cos(x)}

Evaluate the product

f(x)[C] = {sin(x)cos(x) − sin²(x), sin²(x) + sin(x)cos(x)}

Hence, the values of f(x)[B] and f(x)[C] are {sin²(x) + sin(x)cos(x), sin(x)cos(x)} and {sin(x)cos(x) − sin²(x), sin²(x) + sin(x)cos(x)}, respectively

Read more about trigonometry ratios at:

brainly.com/question/11967894

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