Question

Sin^2(π/3) =

A. 1 + cos^2(π/3)
B. 1 - cos^2(π/3)
C. 1 - sec^2(π/3)
D. 1 + sec^2(π/3)

Answer 1

The correct relationship between sin²(π/3) and cos²(π/3) is given by the Pythagorean identity as sin²(π/3) = 1 - cos²(π/3), which corresponds to option B.

Step-by-step explanation:

The student has asked about the relationship between sin2(π/3) and cos2(π/3). Using the Pythagorean identity which states sin2θ + cos2θ = 1, we can rearrange this to sin2(θ) = 1 - cos2(θ). Substituting π/3 for θ, we get sin2(π/3) = 1 - cos2(π/3). Therefore, the correct answer to the student's question is B. 1 - cos2(π/3).