Question

Select the best answer.
cos(3pi/2 + x) =
A. -cosx
B.sinx
C.cosx
D.-sinx

Answer 1

To find cos(3π/2 + x), the cosine sum formula is applied, which simplifies to sin(x). Thus, the correct answer is B. sin(x).

Step-by-step explanation:

The question asks to select the best answer for the expression cos(3π/2 + x). To solve this, we need to know the cosine sum formula, which states that cos(a + b) = cos(a)cos(b) - sin(a)sin(b). When we apply this to the given expression, we get:

• cos(3π/2)cos(x) - sin(3π/2)sin(x)

Since cos(3π/2) = 0 and sin(3π/2) = -1, the expression simplifies to:

• 0 ∙ cos(x) - (-1) ∙ sin(x)
• sin(x)

Therefore, the correct answer is B. sin(x).