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.

the arc length is found by finding the circumference of the full circle (2xpixradius) and then dividing by 4 to find just one quarter of the circle (90 degrees).

in mathematics, a constraint is a condition of an optimization problem that the solution must satisfy. there are several types of constraints—primarily equality constraints, inequality constraints, and integer constraints. the set of candidate solutions that satisfy all constraints is called the feasible set.

hoped i'm right lol