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sin⁡(x)=0.5\sin(x) = 0.5

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Full solution

Q. sin⁡(x)=0.5\sin(x) = 0.5
  1. Identify Relationship: Identify the relationship between sine and cosine for complementary angles.\newlineUsing the identity sin⁡(90°−x)=cos⁡(x)\sin(90° - x) = \cos(x), we can find cos⁡(90°−x)\cos(90° - x) by knowing the value of sin⁡(x)\sin(x).
  2. Use Complementary Angle Identity: Given that sin⁡(x)=0.5\sin(x) = 0.5, we can use the complementary angle identity to find cos⁡(90°−x)\cos(90° - x).\newlineSince sin⁡(x)=cos⁡(90°−x)\sin(x) = \cos(90° - x), we have cos⁡(90°−x)=sin⁡(x)=0.5\cos(90° - x) = \sin(x) = 0.5.
  3. Check Valid Sine Value: Check if the value of sin⁡(x)\sin(x) is within the valid range for sine values.\newlineThe sine of an angle can range from −1-1 to 11, so a value of 0.50.5 is valid.

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