Homework Help: Pre-Calc Homework Help

1. Nov 6, 2004

math_fortress

Simplify the given expression:
2) (sec^2 x)(csc x)/(csc^2 x)(sec x)

2. Nov 6, 2004

arildno

What have you tried?

3. Nov 6, 2004

math_fortress

well...i've done this:

(tan^2 x + 1)(csc x)/(cot^2 x + 1)(sec x)

but...i don't know if i'm going in the right direction, for my teacher is horrible, and i don't know where to go from here if i am going in the right direction

any help would be greatly appreciated

4. Nov 6, 2004

arildno

OK: Let's make the EASIEST cancellations first:
If you look at the expression like this:
$$\frac{sec^{2}(x)csc(x)}{sec(x)csc^{2}(x)}$$

isn't there a couple of cancellations which immediately spring to your mind?

5. Nov 6, 2004

math_fortress

so is it (sec x)/(csc x) ???

6. Nov 6, 2004

arildno

Precisely!
Now, knowing the relation between sec and cos and csc and sin, can you simplify even further?

7. Nov 6, 2004

math_fortress

well, since sin/cos = tan....then would sec/csc = 1/tan ?

That's all i can think of

8. Nov 6, 2004

arildno

No, you have:
$$\frac{\frac{1}{\cos(x)}}{\frac{1}{\sin(x)}}=\frac{1}{\cos(x)}\frac{1}{\frac{1}{\sin(x)}}=\frac{\sin(x)}{\cos(x)}=tan(x)$$

9. Nov 6, 2004

math_fortress

alright...thanks, i'm starting to get it a little better....

10. Nov 6, 2004

math_fortress

Wait...this baffles me...

26.) Find the exact value of sin 5pi/12

Is there any way to do this logically w/ a calculator or anything?

11. Nov 6, 2004

cepheid

Staff Emeritus
Of course there is! (hopefully you meant without a calculator) That's why the angle is given to you in radians, as a rational multiple of $\pi$.

Draw the unit circle: what coordinate points do certain angles represent? $\pi, \frac{\pi}{6}, \frac{\pi}{4}, \frac{\pi}{3}, \frac{\pi}{2}$ etc.

12. Nov 6, 2004

math_fortress

but 5pi/12 isn't on my unit circle...the one's you listed are though...i just don't get how exactly you can find 5pi/12 with information of pi/2, etc...

13. Nov 6, 2004

math_fortress

would 1/4 make sense for the answer since i got the sin of 5pi/6 to equal 1/2?

Last edited: Nov 6, 2004
14. Nov 6, 2004

Sirus

Try to do this using the trig identity
$$\cos{2a}=1-2\sin^{2}{a}$$

15. Nov 6, 2004

math_fortress

What? So you're saying 1/4 isn't right then?
Do I even need to use trig identities for this type of question?

(I'm not arguing with that identity..i'm just very confused )

Last edited: Nov 6, 2004
16. Nov 6, 2004

Sirus

1/4 is incorrect. Sometimes identities are necessary.

17. Nov 6, 2004

cepheid

Staff Emeritus
Yeah, sorry if I gave you the wrong idea. 1/4 is incorrect. You are making the assumption that if I halve the angle, I halve the sine. You can see why that would only be true for a linear relationship right? (which sine is not). I think Sirus has the right technique, since the trig identity involves a term with twice the angle and another with just the angle itself. We know how to work with $\frac{\pi}{6}$, and multiples of it, so find the cosine of the angle $\frac{\5pi}{6}$ and work from there.

18. Nov 7, 2004

kreil

Another way is to convert the radians to degrees and work from there:

sin5pi/12=sin5(180)/12=sin75=sin(30+45)

now you can just use the formula for the sum of angles:
sin (a+b) = cos(b) sin(a) + sin(b) cos(a)

19. Nov 7, 2004

Leaping antalope

use the sum formulas of trig:
sin (a+b)=sin(a) cos(b)+cos(a) sin (b)

now, sin 5pi/12=sin (2pi/12 + 3pi/12), so the exact value of sin 5pi/12 is?

20. Nov 7, 2004

math_fortress

alright....root 2/4 + root 6/4

Thanks for all help