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What is the value of sin(pi - alpha) if sin(alpha) = 5/13?

Mathematics

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Answer

C. 513\text{C. } \frac{5}{13}

Step-by-step solution

3 steps

To solve this problem, we will use a trigonometric identity.

  1. Recall the trigonometric identity for sin⁡(π−θ)\sin(\pi - \theta).

    The identity states that for any angle θ\theta,

    sin⁡(π−θ)=sin⁡θ\sin(\pi - \theta) = \sin \theta
  2. Apply the identity to the given expression.

    In this problem, θ=α\theta = \alpha. So, we can write:

    sin⁡(π−α)=sin⁡α\sin(\pi - \alpha) = \sin \alpha
  3. Substitute the given value of sin⁡α\sin \alpha.

    We are given that sin⁡α=513\sin \alpha = \frac{5}{13}. Substituting this value:

    sin⁡(π−α)=513\sin(\pi - \alpha) = \frac{5}{13}

    Comparing this result with the given options, it matches option C.

    The final answer is C. 513\text{C. } \frac{5}{13}.

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