Question

sin((7pi)/12) = ±sqrt[(1-cos((7pi)/6)/2] =..... here I get confused because cos((7pi)/6)=-(sqrt3)/2. The book says that it's positive though, "because the angle is in quadrant I, sine will be positive." Explain this to me please? I don't quite understand what the hell they're talking about or referring to specifically like where that's supposed to factor in....

Answer 1

That's the whole answer from my textbook thanks james ya always here for me

Answer 2

Once again, your book is crap.

Answer 3

...but good for you: you are right.

Answer 4

i.e., cos(7pi/6) is negative.

Now as for sin(7pi/12), this is an angle not in the first quadrant, but the second quadrant.

Answer 5

because angles from 0 to pi/2 are in the first quadrant; pi/2 to pi are in the second

Answer 6

and sin of any angle in either the first or second quadrant is positive.

Answer 7

you can see that by going back to the definition of sin using the unit circle.

The sin of an angle on the unit circle theta with coordinates (x,y) is y/1 = y.

For the 1st and 2nd quadrants, y is necessarily positive (or zero if you are at exactly theta = 0 or pi)

Answer 8

Thus if you've solved the problem as far as
sin((7pi)/12) = ±sqrt[(1-cos((7pi)/6)/2]
you know you need to choose the positive root because sin(7pi/12) > 0

Answer 9

wow i wish i could call the company and give them a boatload of pellet for this but i looked up reviews on amazon already for this precise reason and some guy said he did just that and they didn't care they just said they had like a website with corrections... which nobody would know about... you don't buy a book if you wanted to use a website... they should have just edited it right holy pellet

Answer 10

and thanks again for your clarification

Answer 11

So ultimately the answer will be ±sqrt[(2+sqrt3)/4] ?

Answer 12

No, you choose either +expression or -expression. But we know that sin(7pi/12) > 0. Hence it must be .... what?

Answer 13

oh right right so it's positive same answer

Answer 14

Yes, that's right.

Answer 15

real quick is that the same as [sqrt(2+sqrt3)]/4 ?

Answer 16

no, because sqrt(4) = 2, not 4.

Answer 17

yeah.... i know... that's how they translated their final answer though and i do get confused with the fundamentals sometimes so i just thought i would aaaask

Answer 18

sure

Now I think I'm seriously overdue a "good answer"

Answer 19

oh pellet i'm sorry haha really sorry that's the sure truth i'm gonna good answer all of yours