Find an angle $\theta$ with $0^{\circ}< \theta< 360^{\circ}$ that has the same:
Sine as $10^{\circ}: \theta=$ degrees
Cosine as $10^{\circ}: \theta=$ degrees
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Answer
The angle that has the same sine as \(10^\circ\) is \(\boxed{170^\circ}\) and the angle that has the same cosine as \(10^\circ\) is \(\boxed{350^\circ}\).
Step 1 ：The sine function has the property that \(\sin(\theta) = \sin(180^\circ-\theta)\) for \(0^\circ<\theta<180^\circ\). Therefore, the angle that has the same sine as \(10^\circ\) is \(180^\circ-10^\circ=170^\circ\).
Step 2 ：The cosine function has the property that \(\cos(\theta) = \cos(360^\circ-\theta)\) for \(0^\circ<\theta<360^\circ\). Therefore, the angle that has the same cosine as \(10^\circ\) is \(360^\circ-10^\circ=350^\circ\).
Step 3 ：The angle that has the same sine as \(10^\circ\) is \(\boxed{170^\circ}\) and the angle that has the same cosine as \(10^\circ\) is \(\boxed{350^\circ}\).
