Question

If cos A = 1/3 , then what is the positive value of sin 1/2​A, in simplest radical form with a rational denominator?

Answer 1

Answer:

Step-by-step explanation:

You should remember from theory (one is the formula of the cosine of the double angle, and the other is the classic sum of squares being 1). $cos A = cos^2 \frac A2 - sin^2 \frac A2 = 1- 2sin^2 \frac A2$

At this point let's grab the first and last step of the chain, replacing values:

$\frac 13 = 1-2sin^2\frac A2 \rightarrow 2sin^2 \frac A2 =\frac23\\sin^2 \frac A2 = \frac13 \rightarrow sin \frac A2 = \frac{1}{\sqrt3} = \frac{\sqrt3}{3}$

Last passage you multiply top and bottom by the square root of 3 to rationalize.