Question

algebra iih - kung - 02 (lms)
alg. iih: 7 - 2 evaluating trigonometric functions: day 1: mathxl (
how many coterminal angles does a given angle have? explain.
o b. infinitely many; any given angle has an infinite number of coterminal angles
o c. three; there is a coterminal angle in each quadrant with the same acute ang angles in all four quadrants.
o d. infinitely many: any given angle can be made coterminal with any other given

Explanation:

Step1: Recall the definition of coterminal angles

Coterminal angles are angles that share the same terminal side. If an angle \(\theta\) is given, then angles of the form \(\theta + 360^{\circ}n\) (where \(n\in\mathbb{Z}\), the set of integers) are coterminal with \(\theta\).

Step2: Analyze the number of possible values for \(n\)

Since \(n\) can take on infinitely many integer values (e.g., \(n = 0,\pm1,\pm2,\pm3,\cdots\)), there are infinitely many angles of the form \(\theta + 360^{\circ}n\).

Answer:

B. Infinitely many; any given angle has an infinite number of coterminal angles