Question

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

Answer 1

Answer:

The positive value is 1/2

Step-by-step explanation:

we know that

The  sine of a half-angle identity is given by the formula

$sin^2(\frac{A}{2})=\frac{1-cos(A)}{2}$

we have

$cos(A)=\frac{1}{2}$

substitute

$sin^2(\frac{A}{2})=\frac{1-\frac{1}{2}}{2}$

$sin^2(\frac{A}{2})=\frac{\frac{1}{2}}{2}$

$sin^2(\frac{A}{2})=\frac{1}{4}$

square root both sides

$sin(\frac{A}{2})=\pm\frac{1}{2}$

therefore

The positive value is 1/2