EXAMELE 17 If $$ \sin 14^{\circ}=k $$, write the (A) $$ \sin 194^{\circ} $$

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To find $$ \sin 194^{\circ} $$ using the known value $$ \sin 14^{\circ} = k $$, we can use the sine angle addition and subtraction identities.

1. **Identify the relationship**: 
   We know that $$ 194^{\circ} $$ can be expressed in terms of $$ 14^{\circ} $$:
   $$
   194^{\circ} = 180^{\circ} + 14^{\circ}
   $$

2. **Use the sine identity**:
   The sine of an angle that is $$ 180^{\circ} + x $$ is given by:
   $$
   \sin(180^{\circ} + x) = -\sin(x)
   $$
   Therefore:
   $$
   \sin(194^{\circ}) = \sin(180^{\circ} + 14^{\circ}) = -\sin(14^{\circ})
   $$

3. **Substitute the known value**:
   Since $$ \sin(14^{\circ}) = k $$, we can substitute this into our equation:
   $$
   \sin(194^{\circ}) = -k
   $$

Thus, the final answer is:
$$
\sin 194^{\circ} = -k
$$
$$ \sin 194^{\circ} = -k $$

EXAMELE 17 If \( \sin 14^{\circ}=k \), write the (A) \( \sin 194^{\circ} \)

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