Question

WILL AWARD MEDAL AND FAN! Can someone please explain step by step how to solve this? This is using double and half angle identities. For some reason i am getting the wrong answer for this...

Answer 1

first you need to know that \(\cos(A)=\frac{12}{13}\)

Answer 2

then use the half angle formula

Answer 3

Ok i did that and got it wrong

Answer 4

did you write
\[\sin(\frac{A}{2})=\sqrt{\frac{1-\frac{12}{13}}{2}}\]?

Answer 5

yes but because it is in quadrant 1 i wrote 1 + 12/13

Answer 6

no

Answer 7

half angle formula for sine has a minus sign inside the radical
for cosine it is plus

Answer 8

So its not 1+ 12/13 for the numerator?

Answer 9

no that is for the half angle formula for cosine

Answer 10

the fact that it is in quadrant one tells you two things
first that
\[\cos(A)=\frac{12}{13}\] and second that it is the positive square root, not the negative one

Answer 11

but the half angle formula for sine is
\[\sin(A)=\sqrt{\frac{1-\cos(A)}{2}}\]

Answer 12

so is the answer 1/sqrt26? i feel like i did that wrong...

Answer 13

???

Answer 14

never mind thanks my answer is correct!