help???

[britttt]

cos (x)/ 1-sin^2 (x)?

 

[mmm4444bot]

Ha! I found an electrical outlet in the parking lot, so now I'm just waiting for my ride.

From your last thread, it seems that you already know the following identity:

1 - [sin(x)]^2 = [cos(x)]^2

Did you try making this substitution, in the current exercise?

 

[britttt]

no...it's like the same as the other problem....the expression cos (x)/ 1-sin^2 (x) is equivalent to

a. cos (x)
b. csc (x)
c. tan (x)
d. sec (x)

 

[mmm4444bot]

As an aside, here's a note about notation (when texting math expressions). Always type grouping symbols around a denominator (or numerator) that contains more than one term.

cos (x)/ 1-sin^2 (x)?

According to the Order of Operations, what you texted above means this:

\(\displaystyle \frac{cos(x)}{1} - sin^2(x)\)

What you intend to type is this:

cos(x)/[1 - sin^2(x)]

which means

\(\displaystyle \frac{cos(x)}{1 - sin^2(x)}\)

I hope that you understand the difference.

 

[britttt]

Oh ok...I see the difference.

 

[mmm4444bot]

no...it's like the same as the other problem....the expression cos (x)/ 1-sin^2 (x) is equivalent to

a. cos (x)
b. csc (x)
c. tan (x)
d. sec (x)

Got it.

In the denominator of the given expression, we see \(\displaystyle 1 - sin^2(x)\)

That expression is an identity for \(\displaystyle cos^2(x)\)

This means that you may substitute \(\displaystyle cos^2(x)\), for the denominator.

Try that. :cool:

 

[HallsofIvy]

mmm444bot said

Ha! I found an electrical outlet in the parking lot, so now I'm just waiting for my ride.

From your last thread, it seems that you already know the following identity:

1 - [sin(x)]^2 = [cos(x)]^2

Did you try making this substitution, in the current exercise?

and your response was

no...it's like the same as the other problem....the expression cos (x)/ 1-sin^2 (x) is equivalent to

a. cos (x)
b. csc (x)
c. tan (x)
d. sec (x)

What do you mean "no"? How about just doing what mmm444bot suggested?

 

[britttt]

Ok...now would I change cos (x) to 1/sec (x)?

 

[mmm4444bot]

I'm not sure why you're thinking about 1/sec(x).

If you arrived at cos(x)/[cos(x)]^2, after the substitution, then that simplifies to 1/cos(x).

There is an identity for 1/cos(x).

 

[mmm4444bot]

My ride's here; gotta go.

Good luck, for now. :cool:

 

[HallsofIvy]

Ok...now would I change cos (x) to 1/sec (x)?

Yes. Or you could change 1/sec (x) to cos(x)!