OpenStudy (anonymous):

cscx cotx(1-cos^2x)=_____x Fill in the blank

2 years ago
OpenStudy (luffingsails):

try expanding each expression: cscx = ? (1/sinx, right?) cotx = ? (1/tanx, right) 1-cos^2x = ? (sin^2x, right?) Then see how it goes from there.

2 years ago
OpenStudy (anonymous):

im thinking ... csc^2x

2 years ago
OpenStudy (luffingsails):

Let's see: cotx = 1/tanx = cosx/sinx, then all it looks like 1/sinx * cos x/sinx * sin^2x Which simplifies to cos(x)

2 years ago
OpenStudy (anonymous):

so final is cscx cotx(1-cos^2x)=cosx

2 years ago
OpenStudy (luffingsails):

Yes.

2 years ago
OpenStudy (anonymous):

thank you

2 years ago
OpenStudy (anonymous):

do you think you could help me with another?

2 years ago
OpenStudy (luffingsails):

Sure, go ahead.

2 years ago
OpenStudy (anonymous):

@luffingsails cos9/2=+-sqrt1+cosa/2 for all values of a T/F

2 years ago
OpenStudy (luffingsails):

Looking. One sec.

2 years ago
OpenStudy (luffingsails):

Is that cos(a/2) or cos(9/2)?

2 years ago
OpenStudy (anonymous):

sorry, it is cos(a/2)

2 years ago
OpenStudy (luffingsails):

Whew... lol.

2 years ago
OpenStudy (luffingsails):

I think it is false, If I just substitute a value in for a (like a=10). It proves false.

2 years ago
OpenStudy (anonymous):

I have 4 more problems.. one is just like the one we just did.

2 years ago
OpenStudy (anonymous):

sin(a+b)=sinacosb-cosasinb for all values of a and b. T/F

2 years ago
OpenStudy (anonymous):

@luffingsails

2 years ago
OpenStudy (luffingsails):

sin(a+b) = sin(a)cos(b) + cos(a)sin(b). So false.

2 years ago
OpenStudy (luffingsails):

Sorry, my work keeps dumping me off of the site. IT security doesn't like open study. lol

2 years ago
OpenStudy (anonymous):

oh ok, i just didn't know if you left me.. you are the first person to ever answer me on here. so your help is greatly appreciated. if cosx=2/3 and x is in quadrant 4, then sin x/2=____

2 years ago
OpenStudy (luffingsails):

No problem. Happy to help.

2 years ago
OpenStudy (luffingsails):

So, remember that cos and sine and all of those deal with right triangle (in the unit circle). So, when you have the cos (x) = 2/3 that is the same as saying adjacent side (2) over hypotenuse (3). All you have to do is solve the right triangle for the 3rd side.

2 years ago
OpenStudy (luffingsails):

3^2 = x^2 + 2^2 9 = x^2 + 4 x^2 = 9 - 4 x^2 = 5 x = sqrt(5)

2 years ago
OpenStudy (luffingsails):

x values in the fourth quadrant are the same as in the first (always positive).

2 years ago
OpenStudy (anonymous):

when i did sqrt(5) i got 2.23 but my answer choices are -1/3 1/3 sqrt1/6 -sqrt1/6

2 years ago
OpenStudy (luffingsails):

Yes, because they are asking what the sin(x/2) is equal to. I gave you what x was equal to.

2 years ago
OpenStudy (anonymous):

so its 1/3?

2 years ago
OpenStudy (anonymous):

@luffingsails

2 years ago