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

1 Answer

3 votes

Answer:

cos 60° = 1/2

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

User Rahman Rezaee
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