Question

plz help: express as a single fraction the exact value of sin 75degrees

Answer 1

hint: 75 = 30 + 45

Answer 2

how?

Answer 3

sum forula for sin.

Answer 4

"formula"

Answer 5

rely?

Answer 6

idk this formula

Answer 7

sin(α + β) = sin(α)cos(β) + cos(α)sin(β)

http://www.purplemath.com/modules/idents.htm

Answer 8

What pgpilot is referring to is the formula

sin (a-b) = sin a cos b - cos a sin b.
pgpilot correctly split up 75 degrees into 45 and 30 by subtraction.

Answer 9

addition dude

Answer 10

oh but how do u no to use tht formula specially?

Answer 11

sin(α + β) = sin(α)cos(β) + cos(α)sin(β) is related... and is more appropriate .... as pgpilot has reminded this "dude."
\
75 = 45 + 30.

@lyubas: stop and think for a moment. What's the next step, now that you ahve the proper formula?

Answer 12

@mathmale , no offense intended!!!

Answer 13

but how do u no to use tht formula specially?

Answer 14

All I can say is that it comes with practice. sin 75 is hard to evaluate, but if you break up 75 into the angles 45 and 30 degrees, whose sines and cosines are easily remembered, you have a formula by which to find sin 75.

sin 75 = sin ( ? + ? ) @lyubas: Can you fill in the missing quantities?

@pgpilot326: Absolutely no offense taken. Thank you for putting me back on track and forgive me for jumping into your discussion with @lyubas.

Answer 15

sin(75) = sin(30+45)= fill in the rest using the formula

Answer 16

@lyubas: I have a job for you (that was one of my father's favorite sayings):

find sin 30, sin 45, cos 30 and cos 45. You'll need them to complete this problem.

Answer 17

@mathmale you're welcome to jump in anytime. you gave me quite the chuckle!

@lyubas is this (the math) making sense?

Answer 18

yes it is

Answer 19

so I got sin75=45+30=sin45cos30+cos30sin45

Answer 20

sin30=radical1/2 sin45 radical 2/2 cos30radical3/2

Answer 21

cos45=radical2/2

Answer 22

sorry to be picking on you, but some of sin75=45+30=sin45cos30+cos30sin45 is out of order.

sin 75 = sin (45 + 30) = sin 45 cos 30 + (you finish)

Answer 23

\[\cos 45\deg=\frac{ \sqrt{2} }{ 2 }\]

Answer 24

Right! what about sin 45 deg? cos 30 deg? cos 45 deg?

Answer 25

sin30=radical1/2 sin45 radical 2/2 cos30radical3/2

Answer 26

sin 75 = sin (45 + 30) = sin 45 cos 30 +cos45sin30

Answer 27

correct?

Answer 28

Nevermind. I didn't see that you'd already typed in your answers. Plese proceed....evaluate sin 75 deg using the formula which our friend @pgpilot326 has provided.

Answer 29

yes, good job

Answer 30

Yes, now you have that correct.

Can you now evaluate sin 75? sin 75 = ( )*( ) + ( )*( )

Answer 31

\[\sin 75=\sin 75=\sqrt{2/2}(\sqrt{3/2)}+\sqrt{2/2 (\sqrt{1/2}}\]

Answer 32

i believe you have the right idea but perhaps need a little work on using latex.

is this what you mean...\[\sin75=\frac{ \sqrt{2} }{ 2 }\cdot\frac{ \sqrt{3} }{ 2 }+\frac{ \sqrt{2} }{ 2 }\cdot\frac{ 1 }{ 2 }\]

Answer 33

yesss lol sry

Answer 34

okay, then all you have left to do is to simplify the expression on the right.

Answer 35

how do I multiply the radicals?

Answer 36

So, lyubas, can you do the multiplication indicated, and then, as pgpilot says, simplify the resulting expression on the right?

Answer 37

\[\sqrt{a}\cdot \sqrt{b}=\sqrt{a\cdot b}\]

Answer 38

or you can factor... it doesn't matter it should be the same number

Answer 39

thanks for the gumball, Mickey!

Answer 40

i stil dnt gt how to multiply radical2/2 amd radical3/2?

Answer 41

if you notice, both terms will have a denominator of 4.

\(\sqrt{2}\cdot\sqrt{3}=\sqrt{2\cdot 3}=\sqrt{6}\)

Answer 42

so you should get\[\sin 75=\frac{ \sqrt{6}+\sqrt{2} }{ 4 }\]

Answer 43

oh gt it radical6/4?

Answer 44

sin75=raidcal8/4?

Answer 45

thts what i got

Answer 46

can i divide on both sides now?

Answer 47

and the \(\sqrt{2}\) comes from the second term (which also has a denominator of 4).

you can't add \(\sqrt{6}+sqrt{2}\) and get \(\sqrt{8}\). doesn't work that way. if it did, then \(\sqrt{4}+\sqrt{4}=\sqrt{8}\) but \(\sqrt{4}+\sqrt{4}=2=2=4\ne\sqrt{8}\)

Answer 48

oops...
\(\sqrt{4}+\sqrt{4}=\sqrt{8}\) but \(\sqrt{4}+\sqrt{4}=2+2=4\ne\sqrt{8}\)

Answer 49

ok so what cani do next?

Answer 50

now i have: sin75=radical8/4 what do i do next?

Answer 51

that's it...
\[\sin75=\frac{ \sqrt{6}+\sqrt{2} }{4 }\]

Answer 52

ohh i gt it lol u cnt relty do anything afta so u jst leave it!

Answer 53

again, no \(\sqrt{8}\) you can't combine like that. they're not like terms.

here's a link to a page to refresh your memory on radicals...
http://www.purplemath.com/modules/radicals3.htm

Answer 54

ye ik tht was a mistake

Answer 55

canu help me with another rques?

Answer 56

plz

Answer 57

it's okay, but you may want to refresh your memory anyways! that's why I'm on this site actually... to stay fresh and sharp on my math skills!

I'm actually leaving so let's call back @mathmale and see if that "dude" can give you a hand!

Answer 58

good luck and happy learning!

Answer 59

oh ok thnks for helping ur awesomew

Answer 60

thanks!