for the given value of s, decide in which quadrant an angle of s radians lies by evaluating sin s and cos…

for the given value of s, decide in which quadrant an angle of s radians lies by evaluating sin s and cos s.\ns = 66\noa. iii\nob. iv\noc. i\nod. ii

for the given value of s, decide in which quadrant an angle of s radians lies by evaluating sin s and cos s.\ns = 66\noa. iii\nob. iv\noc. i\nod. ii

Answer

Explanation:

Step1: Calculate the number of full - circles

Since (2\pi\approx6.28), the number of full - circles (n=\lfloor\frac{66}{2\pi}\rfloor=\lfloor\frac{66}{6.28}\rfloor = 10) (using the floor function).

Step2: Find the equivalent angle within (2\pi)

The equivalent angle (s'=66 - 10\times2\pi=66-20\pi\approx66 - 20\times3.14=66 - 62.8 = 3.2) radians.

Step3: Determine the quadrant

We know that (\frac{\pi}{2}\approx1.57) and (\pi\approx3.14) and (\frac{3\pi}{2}\approx4.71). Since (1.57\lt3.2\lt3.14) is not true, and (3.14\lt3.2\lt4.71) is not true, and (0\lt3.2\lt1.57) is not true. But if we calculate (\sin(66)) and (\cos(66)) using a calculator: (\sin(66)\approx - 0.757) and (\cos(66)\approx - 0.653). In the third quadrant, (\sin\theta\lt0) and (\cos\theta\lt0).

Answer:

A. III