question 23 (1 point)\nthe smallest positive co - terminal angle to - 45° is\na) 45°\nb) 225°\nc) 315°\nd)…

question 23 (1 point)\nthe smallest positive co - terminal angle to - 45° is\na) 45°\nb) 225°\nc) 315°\nd) 405°

question 23 (1 point)\nthe smallest positive co - terminal angle to - 45° is\na) 45°\nb) 225°\nc) 315°\nd) 405°

Answer

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}). [ \begin{align*} \alpha&=360^{\circ}-45^{\circ}\ &=315^{\circ} \end{align*} ] 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})