Question

which angle is coterminal with 170°? -190° -350° -450°

Explanation:

Step1: Recall the formula for coterminal angles

Coterminal angles can be found by the formula \(\theta\pm n\times360^{\circ}\), where \(n = 1,2,3,\cdots\)

Step2: Check each option

• For \(- 190^{\circ}\):

Let \(170^{\circ}+n\times360^{\circ}=-190^{\circ}\), then \(n\times360^{\circ}=-190^{\circ}-170^{\circ}=-360^{\circ}\), \(n = - 1\). But \(\vert n\vert=1\), and \(170^{\circ}+(-1)\times360^{\circ}=170^{\circ}-360^{\circ}=-190^{\circ}\)

• For \(-350^{\circ}\):

Let \(170^{\circ}+n\times360^{\circ}=-350^{\circ}\), then \(n\times360^{\circ}=-350^{\circ}-170^{\circ}=-520^{\circ}\), \(n=-\frac{520^{\circ}}{360^{\circ}}
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• For \(-450^{\circ}\):

Let \(170^{\circ}+n\times360^{\circ}=-450^{\circ}\), then \(n\times360^{\circ}=-450^{\circ}-170^{\circ}=-620^{\circ}\), \(n =-\frac{620^{\circ}}{360^{\circ}}
otin\mathbb{Z}\)

Answer:

\(-190^{\circ}\)