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

11 months ago
satellite73 (satellite73):

half angle formula here, you know it?

11 months ago

Yes!

11 months ago
satellite73 (satellite73):

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

11 months ago
satellite73 (satellite73):

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

11 months ago

So when I plug it in is u 9/41? I am confused on the plugging in

11 months ago
satellite73 (satellite73):

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

11 months ago
satellite73 (satellite73):

hold up

11 months ago
satellite73 (satellite73):

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

11 months ago

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

11 months ago
satellite73 (satellite73):

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

11 months ago
satellite73 (satellite73):

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

11 months ago
satellite73 (satellite73):

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

11 months ago
satellite73 (satellite73):

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

11 months ago

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?

11 months ago

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

11 months ago
satellite73 (satellite73):

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

11 months ago

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

11 months ago
satellite73 (satellite73):

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

11 months ago

Wait!!!

11 months ago

Sin was actually marked wrong

11 months ago
satellite73 (satellite73):

maybe you have to do some more arithmetic

11 months ago
satellite73 (satellite73):

11 months ago

The very last screenshot you sent

11 months ago
satellite73 (satellite73):

that is only step one

11 months ago

This

11 months ago
satellite73 (satellite73):

you have to do the arithmetic

11 months ago
satellite73 (satellite73):

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

11 months ago
satellite73 (satellite73):

are you using webassign?

11 months ago

Yes!

11 months ago
satellite73 (satellite73):

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

11 months ago
satellite73 (satellite73):

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

11 months ago

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

11 months ago
satellite73 (satellite73):

ok cosine is similar, but the minus is a plus

11 months ago
satellite73 (satellite73):

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

11 months ago

Got it! Thank you so much!

11 months ago
satellite73 (satellite73):

you need tangent too right?

11 months ago

How do I find sin(x) for tan?

11 months ago

Reference triangle?

11 months ago
satellite73 (satellite73):

same way you always do draw a triangle

11 months ago
satellite73 (satellite73):

|dw:1480728032097:dw|

11 months ago

So 40?

11 months ago
satellite73 (satellite73):

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

11 months ago
satellite73 (satellite73):

then $\frac{1-\frac{9}{41}}{\frac{40}{41}}$

11 months ago

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

11 months ago
satellite73 (satellite73):

grrr

11 months ago
satellite73 (satellite73):

it is not the SINE OF 40!!

11 months ago
satellite73 (satellite73):

|dw:1480728204567:dw|

11 months ago

11 months ago

Thank you

11 months ago
satellite73 (satellite73):

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

11 months ago
satellite73 (satellite73):

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

11 months ago

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

11 months ago
satellite73 (satellite73):

your welcome, you too did you get it right?

11 months ago