MATH SOLVE

2 months ago

Q:
# Which of the following is not equal to the other values? cos31.7° cos211.7° cos328.3° cos(-391.7°)

Accepted Solution

A:

Answer:* cos 211.7 not equal the other valuesStep-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