Question

question 23 (1 point)
the smallest positive co - terminal angle to - 45° is
a) 45°
b) 225°
c) 315°
d) 405°

Explanation:

Step1: Recall the formula for co - terminal angles

The formula for co - terminal angles is \(\theta + n\times360^{\circ}\), where \(n\in\mathbb{Z}\) ( \(n\) is an integer). We want to find the smallest positive co - terminal angle of \(- 45^{\circ}\). Let \(\theta=-45^{\circ}\), then we set up the equation \(\alpha=-45^{\circ}+n\times360^{\circ}\), and we want \(\alpha>0\).

Step2: Solve for \(n\)

When \(n = 1\), \(\alpha=-45^{\circ}+360^{\circ}\).

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If \(n = 0\), \(\alpha=-45^{\circ}+0\times360^{\circ}=-45^{\circ}<0\). If \(n = 2\), \(\alpha=-45^{\circ}+2\times360^{\circ}=-45^{\circ}+720^{\circ}=675^{\circ}\), which is larger than \(315^{\circ}\).

Answer:

C. \(315^{\circ}\)