Question

13 multiple choice 1 point in which quadrant does the terminal side of a 36° angle lie? third quadrant first quadrant fourth quadrant second quadrant 14 multiple choice 1 point which of the following angles is not coterminal with the other three? 215° 35° -145° 575°

Explanation:

Question 13

Step1: Recall quadrant angles range

First quadrant: \(0^{\circ}<\theta < 90^{\circ}\), second quadrant: \(90^{\circ}<\theta < 180^{\circ}\), third quadrant: \(180^{\circ}<\theta < 270^{\circ}\), fourth quadrant: \(270^{\circ}<\theta < 360^{\circ}\)

Step2: Check \(36^{\circ}\)

Since \(0^{\circ}<36^{\circ}<90^{\circ}\)

Step1: Formula for coterminal angles

Coterminal angles: \(\alpha=\beta + n\times360^{\circ},n\in\mathbb{Z}\)

Step2: Check each angle

• For \(215^{\circ}\):
• \(215^{\circ}-360^{\circ}=- 145^{\circ}\)
• \(215^{\circ}+360^{\circ}=575^{\circ}\)
• For \(35^{\circ}\):
• \(35^{\circ}+n\times360^{\circ}

eq215^{\circ}, - 145^{\circ},575^{\circ}\) for \(n\in\mathbb{Z}\)

Answer:

first quadrant

Question 14