Which of the following lie in the span of the set{cos2(x),sin2(x)}? Select all that apply. A. cos(2x) B. tan2(x) C. sin2(x)+1 D. sin2(2x)
Question
Which of the following lie in the span of the set {cos2(x), sin2(x)}?
Select all that apply.
A. cos(2x)
B. tan2(x)
C. sin2(x) + 1
D. sin2(2x)
Solution
To determine which of the given options lie in the span of the set {cos2(x), sin2(x)}, we need to check if each option can be expressed as a linear combination of cos2(x) and sin2(x).
A. cos(2x): This option is not in the span of the set {cos2(x), sin2(x)} because it is not a linear combination of cos2(x) and sin2(x).
B. tan2(x): This option is not in the span of the set {cos2(x), sin2(x)} because it is not a linear combination of cos2(x) and sin2(x).
C. sin2(x)+1: This option is in the span of the set {cos2(x), sin2(x)}. We can express sin2(x)+1 as a linear combination of cos2(x) and sin2(x) by noting that sin2(x)+1 = 1cos2(x) + 1sin2(x).
D. sin2(2x): This option is not in the span of the set {cos2(x), sin2(x)} because it is not a linear combination of cos2(x) and sin2(x).
Therefore, the options that lie in the span of the set {cos2(x), sin2(x)} are C. sin2(x)+1.
Similar Questions
Consider the function f: R→R defined by f(x)=sin(x)+cos(2x). Which of the following statements about f(x) is true?
Let f = cos2x, g = sin2x. Which of the following lie in the space spanned by f and g
Let f = cos2x, g = sin2x. Which of the following lie in the space spanned by f and g?Question 7Select one: 𝑁𝑒𝑖𝑡ℎ𝑒𝑟 𝐴 𝑛𝑜𝑟 𝐵 𝐵𝑜𝑡ℎ 𝐴 𝑎𝑛𝑑 𝐵3 + 𝑥2 𝑆𝑖𝑛𝑥
Find the dimension of the subspace U = span{[1, 1, 1], [2, 5, 2], [1, 2, 3]}.Select one:a. 1b. none of the other choices is truec. 3d. 2
Which of the following subsets of R2 are spanning sets? Explain your answer.(a) {(−1, 0), (0, 1)}, (b) {(−1, 1), (1, −1)}, (c) {(−1, 0), (1, 0), (−1, 1)
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.