The given mathematical expression and condition are: 3sin(\alpha + \pi) + 2cos(3\pi/2 + \alpha) and sin(\alpha) = -0.3 Simplify the expression and find its value.

Solution:

• Simplify the expression:
  • Using the identity sin(x + \pi) = -sin(x), we have 3sin(\alpha + \pi) = 3(-sin(\alpha)) = -3sin(\alpha).
  • Using the identity cos(3\pi/2 + x) = sin(x), we have 2cos(3\pi/2 + \alpha) = 2sin(\alpha).
  • Combining these, the expression becomes: -3sin(\alpha) + 2sin(\alpha) = -sin(\alpha).
• Substitute the given value of sin(\alpha):
• We are given that sin(\alpha) = -0.3.
• Substituting this value into the simplified expression -sin(\alpha), we get -(-0.3) = 0.3.

Final Answer: The value of the expression is 0.3.