Question

If sin B = − 1/5 with B in QIII, find the following. cos B/2

Answer 1

Answer:

$- \frac{7}{5 \sqrt{2} }$

Step-by-step explanation:

If B is in third quadrant B/2 will be in second . ((π+B)/2). So cosB/2 will be negative .

Use formula now

$cos \: b = \frac{24}{25} \\ cos \: b = 2cos {}^{2} \frac{b}{2} - 1 = \frac{24}{25} \\ 2cos {}^{2} \frac{b}{2} = { \frac{49}{25} } \\ cos \frac{b}{2} = \sqrt{ \frac{49}{50} }$