Expert: Paul Klarreich - 11/30/2008

Question
hi, im having a hard time with this. please help.

-express pi as:
A. sum of 2 angles
B. difference of 2 angles
C. double angle
D. half angle

-solve for sin, cos, tan values of each item above
-geometrically draw how pi results as you express it in each item above  

Answer
Questioner:   Marga
Category:  Advanced Math
Private:  No
 
Subject:  sum & difference identities
Question:  hi, im having a hard time with this. please help.

-express pi as:
A. sum of 2 angles
B. difference of 2 angles
C. double angle
D. half angle

-solve

>> NO, NO, NO -- you don't solve for these, you COMPUTE them.  Don't misuse the vocabulary.  That how students fail math.

.......................


for sin, cos, tan values of each item above
-geometrically draw how pi results as you express it in each item above

>> Huh?
.............................................
Hi, Marga,

To do these, you are expected to KNOW a few values and identities:

sin pi = 0
cos pi = -1
sin 2pi = 0, etc
cos 2pi = 1
sin pi/2 = 1
cos pi/2 = 0
sin 3pi/2 = -1
cos 3pi/2 = 0

etc.

AND

sin(A +- B),
cos(A +- B)
tan(A +- B)
sin(2A)
cos(2A)
tan(2A)
sin(A/2)
cos(A/2)
tan(A/2)

(If you don't know them, look them up and LEARN THEM.)


Now

A. pi = pi/2 + pi/2 (among other ways.)

sin(pi) = sin(pi/2 + pi/2) = sin pi/2 cos pi/2  + cos pi/2 sin pi/2

Use the above values and compute:

sin(pi) = (1)(0) + (0)(1) = 0

cos(pi) = cos(pi/2 + pi/2) = cos pi/2 cos pi/2  + sin pi/2 sin pi/2

= (I think you get the idea.)


That's the way for all of them.  (It's a bit of work, but you are not afraid of that, are you?)

B. pi = 3pi/2 - pi/2

Do these the same way.

C. pi = 2(pi/2)

D. pi = (2pi)/2

That should do it