Answer:
* cos 211.7 not equal the other values
Step-by-step explanation:
* Lets revise the angles in the four quadrant
- If the angle in the first quadrant is Ф, then the equivalent angles to
it in the other three quadrant are
# 180° - Ф ⇒ 2nd quadrant (sin only +ve)
# 180° + Ф ⇒ 3rd quadrant (tan only +ve)
# 360° - Ф ⇒ 4th quadrant (cos only +ve)
# -Ф ⇒ 4th quadrant (cos only +ve)
# -180 + Ф ⇒ 3rd quadrant (tan only +ve)
# -180 - Ф ⇒ 2nd quadrant (sin only +ve)
# -360 + Ф ⇒ 1st quadrant (all are +ve)
* Lets solve the problem
∵ Ф = 31.7°
∵ cos 31.7 = +ve value
∵ 180° + Ф° = 180° + 31.7° = 211.7°
∵ cos (180° + Ф°) = - cos Ф° ⇒ cos (180° + Ф°) in the 3rd quadrant is
same value as cos Ф but with -ve sign
∴ cos 211.7° = - cos 31.7°
∴ cos 31.7° ≠ cos 211.7°
∵ 360° - Ф° = 360° - 31.7° = 328.3°
∵ cos (360° - Ф°) = cos Ф° ⇒ cos (360° - Ф°) in the 4th quadrant has the
same value and sign with cos Ф°
∴ cos 328.3° = cos 31.7°
∴ cos 31.7° = cos 328.3°
∵ -391.7° + 360° = -31.7° ⇒ more then clockwise turn by 31.7°
∵ cos (-Ф°) = cos Ф° ⇒ cos (-Ф°) in the 4th quadrant has the same value
and sign with cos Ф°
∴ cos (-31.7°) = cos 31.7°
∴ cos 31.7° = cos (-390.7°)
* cos 211.7 not equal the other values
