Question

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

Answer 1

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.

Answer 2

im thinking ... csc^2x

Answer 3

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)

Answer 4

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

Answer 5

Yes.

Answer 6

thank you

Answer 7

do you think you could help me with another?

Answer 8

Sure, go ahead.

Answer 9

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

Answer 10

Looking. One sec.

Answer 11

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

Answer 12

sorry, it is cos(a/2)

Answer 13

Whew... lol.

Answer 14

I think it is false,

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

Answer 15

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

Answer 16

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

Answer 17

@luffingsails

Answer 18

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

Answer 19

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

Answer 20

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=____

Answer 21

No problem. Happy to help.

Answer 22

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.

Answer 23

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

Answer 24

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

Answer 25

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

Answer 26

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

Answer 27

so its 1/3?

Answer 28

@luffingsails