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

cos 60° = 1/2

Step-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