Question

Angle A in Quadrant III and 0°≤A<360°, cosA= -2/5
cos A/2=
a. √7/10
b. √3/10
c. -√3/10
d. -√7/10

Answer 1

It's given that A is in third quadrant, so A would lie between 180 and 270 degrees
\[180\le A \le 270\]
Can you tell the range of A/2 ?

Answer 2

Oh o.k. Wait, the range of A/2?

Answer 3

yeah, like A is from 180 to 270
what would be for A/2?

Answer 4

90 to 135?

Answer 5

good, so what's the sign of cosine in this range?

Answer 6

@mathsux4real what's the sign of cos in II quadrant?

Answer 7

cos(θ) < 0 ?

Answer 8

good:)
so here we would have cos A/2 <0
do yo know the half angle formula for cosine?

Answer 9

Can you give it to me? I don't know it right off the bat

Answer 10

it's given as
\[\Large 2 \cos^2 \frac A 2=1+ \cos A\]

Answer 11

find cos A/2 and remember that it's negative

Answer 12

I can't seem to match it up.

Answer 13

put cos A=-2/5
I think you'd get it.
Try again :)

Answer 14

So 0.6

Answer 15

it's
\[2\times \cos^2 \frac A 2=1+\cos A\]
you have to divide by 2 and then take root

Answer 16

I came up with either 1.825 or 1.35 :/

Answer 17

@dta255 any thoughts?

Answer 18

\[2\times \cos^2 \frac A 2=1-\frac 25\]
\[2\times \cos^2 \frac A 2=\frac 35\]
divide both sides by 2, we get
\[ \cos^2 \frac A 2=\frac 3{10}\]
Taking root both sides, we get
\[ \cos \frac A 2=\pm \sqrt {\frac {3}{10}}\]
Now which sign should we take

Answer 19

+

Answer 20

@mathsux4real here \[\frac A 2\] lies in the second quadrant, then what will be the sign?

Answer 21

-

Answer 22

yes:) do you understand this?

Answer 23

Yes. I looked it up to understand fully. Thank you very much ash

Answer 24

welcome:D