Question

Find the exact values of
sin(u/2), cos(u/2), and tan(u/2)
using the half-angle formulas.


cos u = 9/41, 0 < u < π/2

u/2 lies in quadrant 1

Answer 1

half angle formula here,
you know it?

Answer 2

Yes!

Answer 3

\[\huge \sin(\frac{u}{2})=\sqrt{\frac{1-\cos(u)}{2}}\]

Answer 4

replace \(\cos(u)\) with \(\frac{9}{41}\)

Answer 5

So when I plug it in is u 9/41?

I am confused on the plugging in

Answer 6

\[\sqrt{\frac{1-\cos(u)}{2}}\\
\sqrt{\frac{1-\frac{9}{41}}{2}}\]

Answer 7

hold up

Answer 8

it is not the cosine OF \(\frac{9}{41}\), the cosine IS \(\frac{9}{41}\)

Answer 9

What about the beginning sin(u/2)
Will it be sin(9/41))/2 ?

Answer 10

ok i see this confusion frequently, so lets see if i can say it another way

Answer 11

you are told what the cosine of u is, i.e \[\cos(u)=\frac{9}{41}\] it is that number

Answer 12

all you do is replace \[\cos(u)\] in the formula by the number \(\frac{9}{41}\)

Answer 13

\[\huge \sin(\frac{u}{2})=\sqrt{\frac{1-\cos(u)}{2}}\]
\[\color{red}{\cos(u)}=\color{red}{\frac{9}{41}}\]
\[\huge \sin(\frac{u}{2})=\sqrt{\frac{1-\color{red}{\frac{9}{41}}}{2}}\]

Answer 14

I understand the problem and answer, but how would you write the beginning?

cos(u/2) = .....

cos( <<<This part, like how do I plug that in?

Answer 15

Oh! Okay, so I guess I don't need to plug it in.
It just stays the same?

Answer 16

you have three questions, sine, cosine and tangent of \(\frac{u}{2}\) i wrote the one for sine above

Answer 17

Yes! I understand the rest! Thank you!!!

Answer 18

i can try to say it differently but i don't know how to make it clear.
the cosine of u, you are told that number
you do not take the cosine of that number, it is the number itself

Answer 19

Wait!!!

Answer 20

Sin was actually marked wrong

Answer 21

maybe you have to do some more arithmetic

Answer 22

what did you write as your answer?

Answer 23

The very last screenshot you sent

Answer 24

that is only step one

Answer 25

This

Answer 26

you have to do the arithmetic

Answer 27

oh, also you put that is for cosine
that should have been for sine

Answer 28

are you using webassign?

Answer 29

Yes!

Answer 30

it is very forgiving, maybe it will take that answer, but that answer was for sine, not for cosine
you put it in the wrong box

Answer 31

you might also try \[\frac{4}{\sqrt{41}}\] which looks a lot better

Answer 32

Oh!!! Okay! Yes, it is marked correct for sine now

Answer 33

ok cosine is similar, but the minus is a plus

Answer 34

\[\huge \cos(\frac{u}{2})=\sqrt{\frac{1+\color{red}{\frac{9}{41}}}{2}}\]

Answer 35

Got it! Thank you so much!

Answer 36

you need tangent too right?

Answer 37

How do I find sin(x) for tan?

Answer 38

Reference triangle?

Answer 39

same way you always do
draw a triangle

Answer 40

So 40?

Answer 41

there is actually an easier way, but yeah 40 i think

Answer 42

then \[\frac{1-\frac{9}{41}}{\frac{40}{41}}\]

Answer 43

sin(40)
________
1+ (9/41)

Answer 44

grrr

Answer 45

it is not the SINE OF 40!!

Answer 46

Don't yell please

Answer 47

Thank you

Answer 48

\[\cos(u)=\frac{9}{41}\\
\sin(u)=\frac{40}{41}\]

Answer 49

do not take the sine or cosine of those numbers, those are the numbers you use ...(he said quietly)

Answer 50

Lol! Okay I got it! Thank you! Gave a great day!!! :)

Answer 51

your welcome, you too
did you get it right?

Answer 52

@satellite73 Yes!

Answer 53

yay!!