# 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