For the given value of s, decide in which quadrant an angle of s radians lies by evaluating sin s and cos s.
-s = 66
A)III
B)IV
C)I
D)II

Question

Quizplus · Accepted Answer

To determine the quadrant of an angle measured in radians, we first need to convert the angle to its equivalent within the first full circle (0 to $2\pi$ radians). Given $s = 66$ radians, we reduce this by subtracting multiples of $2\pi$ (approximately 6.283) until the angle falls within the range of 0 to $2\pi$. $66 \mod 2\pi \approx 66 \mod 6.283 \approx 3.115$This result, approximately 3.115 radians, lies in the third quadrant because it is greater than $\pi$ (approximately 3.142) but less than $1.5\pi$ (approximately 4.712). In the third quadrant, both sine and cosine are negative, which aligns with the characteristics of angles in this quadrant.

For the Given Value of S, Decide in Which Quadrant