Q:

If sinx= sqrt(3)/2, and 90° < x < 180°, what is cos(x/2)?

Accepted Solution

A:
Answer:cos 60° = 1/2Step-by-step explanation:* Lets explain how to solve the question- If angle Ф lies in the first quadrant then sin Ф , cos Ф and tan Ф  are positive values- The equivalent angle of angle Ф in the second quadrant is 180° - Ф  and sin Ф is positive but cos Ф and tan Ф are negative- The equivalent angle of angle Ф in the third quadrant is 180° + Ф  and tan Ф is positive but cos Ф and sin Ф are negative- The equivalent angle of angle Ф in the fourth quadrant is 360° - Ф  and cos Ф is positive but sin Ф and tan Ф are negative* Lets solve the problem∵ sin x = √3/2∵ 90° < x < 180°∴ ∠ x lies in the second quadrant∴ m∠ x = 180° - Ф- Let sin Ф = √3/2∴ Ф = sin^-1 (√3/2)∴ Ф = 60°∵ x = 180° - Ф∴ x = 180° - 60°∴ x = 120°- To find cos(x/2) divide 120° by 2∵ cos (120°/2) = cos (60°)∴ cos 60° = 1/2