Question

angle of s radians lies.
s = 67
...
sin s = \square
(round to four decimal places as needed.)
cos s = \square
(round to four decimal places as needed.)
base on the values of sin s and cos s, in which quadrant is an angle of s radians located?
a. quadrant iv
b. quadrant ii
c. quadrant i
d. quadrant iii

Explanation:

Step1: Find the value of \( \sin(67) \)

Using a calculator, \( \sin(67) \approx -0.8555 \) (since \( 67 \) radians is in a position where sine is negative; we know that \( 20\pi \approx 62.83 \), \( 67 - 20\pi \approx 67 - 62.83 = 4.17 \), but actually, more accurately, using calculator input: \( \sin(67) \approx -0.855470958 \), rounded to four decimals is \( -0.8555 \).

Step2: Find the value of \( \cos(67) \)

Using a calculator, \( \cos(67) \approx 0.517350407 \), rounded to four decimals is \( 0.5174 \).

Step3: Determine the quadrant

In quadrant IV, sine is negative and cosine is positive. Since \( \sin(67) \approx -0.8555 \) (negative) and \( \cos(67) \approx 0.5174 \) (positive), the angle is in Quadrant IV.

Answer:

\( \sin s \approx -0.8555 \)
\( \cos s \approx 0.5174 \)
The angle is in A. Quadrant IV