If cos x = 2 / 3 and x is in quadrant 4, find:

a. sin (x / 2)

b. cos (x / 2)

c. tan (x / 2)

A

Step-by-step explanation:

cos (x) = 2/3 in Q 4

sin (x/2) = + √ (1-cos (x)) / 2

√ (1-cos (x)) / 2=√ (1-[2/3]/2=√ (1/3) / 2=-√ (1/6) because sin is negative in Q 4

See below.

Step-by-step explanation:

Because cos x = 2/3 the adjacent side = 2 and hypotenuse = 3 so the length of the opposite side =

√ (3^2 - 2^2) = - √5 (its negative because we are in Quadrant 4).

So sin x = - √5/3.

(a) sin (x / 2) = - √ [ (1 - cos x) / 2 ]

= - √ (1 - 2/3) / 2)

= - √ (1/6). or - 0.4082.

(b) cos (x/2) = √ [ (1 + cos x) / 2]

= √ 5/6 or 0.9129.

(c) tan (x / 2) = (1 - cos x) / sin x.

= (1 - 2/3) / - √5/3

= - 0.4472.