If sec⁡ x=2, and 270°<x<360°, what is sin (x/2)?

Question

If sec⁡ x=2, and 270°<x<360°, what is sin (x/2)?

Answer 1

Hi Alice.

If the sec x = 2, then that means cos x = 1/2 since secant and cosine are reciprocals.

According to the unit circle, if cos x = 1/2, then x is either 60 degrees or 300 degrees. Since we are told that the angle is between 270 and 360, x must be 300.

So, now we are ready to answer the question: sin x/2 =sin 300/2 = sin 150 = 1/2.

Hope this helps! :)

Answer 2

If sex (x) = 2, then cos (x) = 1/2, then x = 60° or 300°. But because 270° < x < 360°, x must be 300°

x = 300°

x/2 = 150°

x/2 = 150° = 180° - 30°

Remember that sin (180° - a) = sin a

sin (x/2) = sin (180° - 30°) = sin (30°) = 1/2

sin (x/2) = 1/2