circle subtended by the angle. (F.TF.A.1,F.TF.A.2) 1. The angle $$ \frac{\pi}{4} $$ radians has the same sine value as which of the following angles? Give an explanation of your answer.

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1. We know that for any angle $$ \theta $$, the sine function satisfies  
   $$
   \sin(\theta) = \sin(\pi - \theta).
   $$
2. If we let $$ \theta = \frac{\pi}{4} $$, then the angle with the same sine value is given by  
   $$
   \pi - \frac{\pi}{4} = \frac{4\pi}{4} - \frac{\pi}{4} = \frac{3\pi}{4}.
   $$
3. On the unit circle, both $$ \frac{\pi}{4} $$ and $$ \frac{3\pi}{4} $$ have the same $$ y $$-coordinate, which is the sine value. Specifically,  
   $$
   \sin\left(\frac{\pi}{4}\right)=\frac{\sqrt{2}}{2} \quad \text{and} \quad \sin\left(\frac{3\pi}{4}\right)=\frac{\sqrt{2}}{2}.
   $$
   
Thus, the angle $$ \frac{\pi}{4} $$ has the same sine value as $$ \frac{3\pi}{4} $$.
The angle $$ \frac{\pi}{4} $$ has the same sine value as $$ \frac{3\pi}{4} $$ because both angles have the same $$ y $$-coordinate on the unit circle, which is $$ \frac{\sqrt{2}}{2} $$.

circle subtended by the angle. (F.TF.A.1,F.TF.A.2) 1. The angle \( \frac{\pi}{4} \) radians has the same sine value as which of the following angles? Give an explanation of your answer.

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