You've Got the Right Angle
Because o f the definitions o f the trigonometric functions, it is more convenient to
deal with trigonometric functions in the context o f right triangles. Here are three
examples.
A
B
c
E
D
Figure 1.6.
E xample 1.1. Figure 1.6
Figure 1.27.
The graphs o f y = s in- 1 (sin x ) , y = c os- 1 ( cosx), Y = sin ( sin- 1 x ) , y =
cos ( cos- 1 x ) , Y = c os- 1 (sin x ) , y = sin - 1 ( cosx) , y = sin ( cos- 1 x ) , and
y = cos (sin - l x ) are interesting and important. We leave it t
In general, because 4 [ABC]
c ot ex
a 2 + b 2 + c2
a2
b2
c2
+ 2ca sin B + -,-,-4 [A B C]
2 bc sin A
2 ab sin C
2A
2B
sin
sin
sin 2 C
2 sin B sin C sin A + 2 sin C sin A sin B + 2 sin A sin B sin C
sin 2 A + sin 2 B + sin 2 C
2 sin A sin B sin C
1
tan ex
=
how can we compute the length o f the shortest path along the surface connecting
the two places? Let C denote this path. Intuitively, it is not difficult to see that the
points on C all lie on a plane. This fact is not that easy to prove, however, so let'
Eunice Wu
Shaneyfelt
Journal Entry 1 : 12-11-10
1. The kind of person I think I am:
Very visual!
i. Art is a big part of my life
ii. A diagram or table works better than a block of text
iii. Enjoy looking at pictures more than reading words most of the
t