Question of sin 23pi/12

Question

dtan5457 · Answer

which is 345 degrees

which is 300 degrees + 45..

dtan5457 · Answer

so the 300 degrees would be negative right? -sqrt3/2?

thesmartone · Answer

sin 300 will be negative as it is in 4th quadrant

thesmartone · Answer

yup -sqrt3/2! :D

dtan5457 · Answer

so i plug into the sum sin formula as negative?

thesmartone · Answer

Well we are dealing with radians, so keep it in radians.

$\sf 23\pi /12 = 2\pi-pi/12$

dtan5457 · Answer

the answer ends up in radians..?

thesmartone · Answer

23pi/12 is radian already

dtan5457 · Answer

still not sure how to solve with sinAcosB+cosAsinB

thesmartone · Answer

$\sf 23pi/12 = 5pi/3 + pi/4$

dtan5457 · Answer

wouldn't you have to simplify out the radians?

thesmartone · Answer

Yes, we would have to.

$\sf sin(5pi/3+pi/4)=sin (5pi/3) cos (pi/4) + cos(5pi/3)sin(pi/4)$

thesmartone · Answer

|dw:1428981185396:dw|

dtan5457 · Answer

i'm getting
$$(\frac{ -\sqrt{3} }{ 2 })(\frac{ \sqrt{2} }{ 2 })+(\frac{ 1 }{ 2 })(\frac{ \sqrt{2} }{ 2 })$$

thesmartone · Answer

$\color{blue}{\text{Originally Posted by}}$ @TheSmartOne
Yes, we would have to.

$\sf sin(5pi/3+pi/4)=sin (5pi/3) cos (pi/4) + cos(5pi/3)sin(pi/4)$
$\color{blue}{\text{End of Quote}}$

$\Large\sf = \frac{-\sqrt{3}}{2}(\frac{ \sqrt{2} }{ 2 })+(\frac{ 1 }{ 2 })(\frac{ \sqrt{2} }{ 2 })$

thesmartone · Answer

correct :)

thesmartone · Answer

So at the end you should get

$\sf\Large\frac{\sqrt{2}-\sqrt{6}}{4}$

thesmartone · Answer

- sqrt 6 + sqrt 2 = sqrt2 - sqrt 6

dtan5457 · Answer

can the answer be $$\frac{ 2\sqrt{2} }{ 4 }$$
that's what the answer key says

dtan5457 · Answer

because i got the same thing as you

dtan5457 · Answer

$$\frac{ -\sqrt{6}+\sqrt{2} }{ 4 }$$
which is the same as yours

thesmartone · Answer

The answer is key is soo wrong.

dtan5457 · Answer

i agree, not even gonna bother with it. gonna go with our answers.

thesmartone · Answer

Our answer will be negative since sqrt 6 is bigger than sqrt 2 and tiny number = big number = negative number The answer key has an answer that is positive. And this also helps our case: http://prntscr.com/6thvjd (made sure it was radians too always have too :P)

dtan5457 · Answer

lol yep, gonna stick with what we got. thank you

thesmartone · Answer

Thank you! This was fun practice for my trig class :D

dtan5457 · Answer

haha np. I got one more that seems a bit harder. will post shortly.

thesmartone · Answer

I gtg now, I'll check it later tomorrow :P

dtan5457 · Answer

alright np.