SOLUTION: Find the exact value of sin (theta)/2 if cos (theta) = 2/3 and 270 deg. < (theta)

SOLUTION: Find the exact value of sin (theta)/2 if cos (theta) = 2/3 and 270 deg. < (theta) < 360 deg.

Question 349082: Find the exact value of sin (theta)/2 if cos (theta) = 2/3 and 270 deg. < (theta) < 360 deg.
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
(For reasons I do not know, Algebra.com's formula software does not do theta, So I will be using alpha, , instead.

The general formula is
(The zero in front is due to another limitation of Algebra.com's software.)
Since is between 270 and 360, sin is negative so we will use:

Replacing with 2/3 we get:

Simplifying:

which is the simplified, exact value for .
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