If the $\sin 0^{\circ}=0$, then which statement is true? ( 1 point $)$ $\cos 90^{\circ}=0$, because the cosine and sine are complements $\cos 180^{\circ}=1$, because the cosine and sine are supplements $\cos 180^{\circ}=0$, because the cosine and sine are supplements $\cos 90^{\circ}=1$, because the cosine and sine are complements
Solution
Step 1 ：The question is asking which of the given statements is true. The statements are about the values of cosine at certain angles. We know that \(\sin 0^\circ=0\), and we need to find which of the given statements about cosine is true.
Step 2 ：We know that the cosine of an angle in a right triangle is the ratio of the adjacent side to the hypotenuse. The cosine of \(90^\circ\) is 0 because at \(90^\circ\), the adjacent side is 0 and the hypotenuse is 1. The cosine of \(180^\circ\) is -1 because at \(180^\circ\), the adjacent side is -1 and the hypotenuse is 1.
Step 3 ：So, we can see that the first and third statements are true. However, the question asks for only one true statement. Therefore, we need to check the reasoning given in the statements. The first statement says that cosine and sine are complements, which is not true because cosine and sine are not always complements. The third statement says that cosine and sine are supplements, which is also not true because cosine and sine are not always supplements.
Step 4 ：The cosine of \(90^\circ\) is approximately 0 and the cosine of \(180^\circ\) is -1. The reasoning given in the first and third statements is incorrect, so neither of these statements is completely true.
Step 5 ：\(\boxed{\text{None of the given statements is true.}}\)
