My math questions are as follows. Find exact values. Angles are in degrees. 
1)(a) Sin (45) (b)Sin (-240) (c)_cos (-30) (d) cos (495) (e) tan (-120)

2) find exaxt values. Angles are in radians.

(a) Sin ( pie) (b) Sin (pie/4) (c) Cos 5pie/4 (d) cos (3pie/2) (e) Tan
(-5pie/6) f) Cos (-pie/3)

5) Convert the following angles to positive angles so that: x is
greater than or equal to 0 degrees and less than or equal to 360
degrees:

(a)-45  b) -135  c) -745

6) Convert the following angles to positive angles so that: x is
greater than or equal to 0 and less than or equal to 2pie:

a) -pie/4 b) -5pie/6  c) -pie/3


 * Most importantly, I need to know the SIMPLEST way to solve these
questions and show all work. I have lots of other questions which i
will also ask if i am satisfied with the results.

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Clarification of Question by harecreek-ga on 09 Jan 2006 21:02 PST

Questions 5 and 6 have been figured out!!!

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Clarification of Question by harecreek-ga on 10 Jan 2006 09:44 PST

As ratty_ mentioned, pi should be spelled without an e at the end.

You should memorise some basic values:

    Angle       Sin         Cos        Tan
(deg) (rad)
   0    0        0           1          0
  30   pi/6     1/2      sqrt(3)/2   1/sqrt(3)
  45   pi/4   1/sqrt(2)  1/sqrt(2)      1
  60   pi/3   sqrt(3)/2     1/2       sqrt(3)
  90   pi/2      1           0       undefined

(Note that most of these values can be derived from one another - for
instance, sin 60 deg = cos 30 deg and vice versa; tan can of course be
derived from sin and cos. You can also get cos 30 deg from sin 30 deg.
Ultimately you can get them all from double and triple angle formulae,
but it's better to know the basic ones.)

You should also know these basic relationships, which you can figure
out by looking at a unit circle for a bit (I'm using radians;
substitue 180 for pi for the same formulae in terms of degrees):

sin (-x) = - sin x; cos (-x) = cos x; tan (-x) = -tan x
sin (pi/2 - x) = cos x; cos (pi/2 - x) = sin x; tan (pi/2 - x) = 1/tan x
sin (pi - x) = sin x; cos (pi - x) = -cos x; tan (pi - x) = -tan x
sin (x + pi) = -sin x; cos (x + pi) = -cos x; tan (x + pi) = tan x
sin (x + 2pi) = sin x; cos (x + 2pi) = cos x; tan (x + 2pi) = tan x

So, for instance:
(degrees - question 1)
 (b): sin (-240) = sin (-240 + 360) = sin (120) = sin (180-120) 
= sin 60 = sqrt(3)/2.
Or, sin (-240) = - sin (240) = - sin (60 + 180) = - (- sin 60)
= sin 60 = sqrt(3)/2.
 (c): cos (-30) = cos(30) = sqrt(3)/2.
 (d): cos (495) = cos(495 - 360) = cos (135) = - cos(180 - 135)
= - cos 45 = -1/sqrt(2).

(radians - question 2)
 (a): sin pi = sin (pi - pi) = sin 0 = 0.
 (b): sin pi/4 = 1.
 (c): cos 5pi/4 = cos (pi + pi/4) = - cos (pi/4) = -1/sqrt(2).
 (e): tan (-5pi/6) = tan (-5pi/6 + pi) = tan (pi/6) = 1/sqrt(3).


 
Question? For radians (question 2) part (a)why is it pi - pi.
 (b) sin pi/4 should not be 1 according to the "memorize basic values section"
 (c) and (d) I do not get those either.

For queestion 1) degrees when and why do you add or subtract 360 and
for (d) why did it all of a sudden become -cosine.

Hi

Actually google will answer most of these directly for you!

Just put into the google search engine, for example, 
  sin(45 degrees)
... and click on Search.

It's dead good, and not a lot of people know about it.

If you want to do Sin(pie), you should spell Pi without the e, so put in:
  sin(pi)

Showing all the working is tricky.
The easiest way is to draw a triangle with the angles you are looking
for, and then remember:
Sin = Opposite / Hypoteneuse
Cos = Adjacent / Hypoteneuse
Tan = Opposite / Adjacent

So, for sin 45 degrees, you would drawer a 45 - 45 - 90 degree (right
angled triangle), make the two short sides =1, use Pythagoras to show
the hyp = sqrt(2) and thus sin(45 degrees) = 1 / sqrt(2).

Ratty

As ratty_ mentioned, pi should be spelled without an e at the end.

You should memorise some basic values:

    Angle       Sin         Cos        Tan
(deg) (rad)
   0    0        0           1          0
  30   pi/6     1/2      sqrt(3)/2   1/sqrt(3)
  45   pi/4   1/sqrt(2)  1/sqrt(2)      1
  60   pi/3   sqrt(3)/2     1/2       sqrt(3)
  90   pi/2      1           0       undefined

(Note that most of these values can be derived from one another - for
instance, sin 60 deg = cos 30 deg and vice versa; tan can of course be
derived from sin and cos. You can also get cos 30 deg from sin 30 deg.
Ultimately you can get them all from double and triple angle formulae,
but it's better to know the basic ones.)

You should also know these basic relationships, which you can figure
out by looking at a unit circle for a bit (I'm using radians;
substitue 180 for pi for the same formulae in terms of degrees):

sin (-x) = - sin x; cos (-x) = cos x; tan (-x) = -tan x
sin (pi/2 - x) = cos x; cos (pi/2 - x) = sin x; tan (pi/2 - x) = 1/tan x
sin (pi - x) = sin x; cos (pi - x) = -cos x; tan (pi - x) = -tan x
sin (x + pi) = -sin x; cos (x + pi) = -cos x; tan (x + pi) = tan x
sin (x + 2pi) = sin x; cos (x + 2pi) = cos x; tan (x + 2pi) = tan x

So, for instance:
(degrees - question 1)
 (b): sin (-240) = sin (-240 + 360) = sin (120) = sin (180-120) 
= sin 60 = sqrt(3)/2.
Or, sin (-240) = - sin (240) = - sin (60 + 180) = - (- sin 60)
= sin 60 = sqrt(3)/2.
 (c): cos (-30) = cos(30) = sqrt(3)/2.
 (d): cos (495) = cos(495 - 360) = cos (135) = - cos(180 - 135)
= - cos 45 = -1/sqrt(2).

(radians - question 2)
 (a): sin pi = sin (pi - pi) = sin 0 = 0.
 (b): sin pi/4 = 1.
 (c): cos 5pi/4 = cos (pi + pi/4) = - cos (pi/4) = -1/sqrt(2).
 (e): tan (-5pi/6) = tan (-5pi/6 + pi) = tan (pi/6) = 1/sqrt(3).

I've left a few for you to do by yourself; if you need any help with
them, or with understanding the steps I've used above, say so and I or
someone else can explain further.