II~
Introduction
-',)"
t.y
to Trigonometry
The field of mathematics
called "Trigonometry"
Key word:
SOH CAH TOA or
is the study of right triangles.
()
A.
C-
,r.,' -
1/
•
slnx
0
opposite (leg )
=----hypotenuse
cosx
s: sine
o
1/
r-()
A
adiacent(le~)
='
'tanx
hypotenuse
0
opposite(/eg)
=----adjacent (leg)
0: opposite leg
A: adjacent leg
H: hypotenuse
(sin)
C: cosine (cas)
T: tangent (tan)
The three sides of the triangles are referred to as Hypotenuse (H), Adjacent (A), and Opposite (0). Label
each side of each triangle using angle Was your reference.
y~,~
A~
z
W
Use the triangle at the right to determine the following
Ph,
sin 400 =
(j)
sin 500 =
y
values.
~1
,.",/
cas 400 = __ IJ'_Jl
tan40o=--
£%1
tan50o=~
'y
B
Write each ratio in simplest form.
~/.5' 2.
1. sin A ~
cos A
lfJ'5
3. tan A
1l.-/.• 2.0
4. sin 8 -:::.
3i.-
lf/s
/5
6. tan 8
*
;1-2~
3
tfiJ
1-6-
A
'-f
In right triangle HLK, name the ratio represented for the given angle.
Get> l.-.~tJ.-7. LH.!2.
'17
Jl.
8. LH ~
'17
~
9. LH ~
'15
12.
/K~~
,
17
L
-to....cf2AJ
6-_
K
C
~
f:S
.. .') 30
(..-,
i __
I
(;L.
..
. ~.)
')
.~
",-
'"
Using special right tria~gleS to write each trigonometric ratio as a fraction.
,i.L
iC.N- 4 s;::.
)j
17. cas 60'
16. tan 45°
I
&')icu':;;J~
P2.
2..•
CC/l " 0 ~ I) 2.
(;c-::;
21. sin 30°
19. cas 45°
18. sin 60°
.
~\J~
2-:
\.\'52-.J
0.-;
U,VJ4S--
. v,",
2
30::;, ,Q..(.
!i
1.......
More Trigonometric Ratios
The cosine, sine and tangent ratios are defined in terms of the lengths of the sides of a right
triangle. Three other ratios are the secant, the cosecant and the cotangent ratios. The ratios
are abbreviated as sec, csc, cot.
sec A =
csc A =
cot A =
length of hypotenuse
length of side adjacent to LA
length of hypotenuse
length of side opposite to LA
length of side adjacent to LA
length of side opposite LA
c
-b
=
=
a
c
a
\'"
J/'
b
A
a
The secant ratio for L A is the reciprocal of its C -.
~
ratio.
The cosecant ratio for L A is the reciprocal of its .,.~'h.J:...,.. ratio.
The cotangent ratio for L A if the reciprocal of its te:...--. \l!.-T ratio.
,/
22. sec A =L,c,o Ii :.. '-II.)
'5/i
25. sec B -;.. 5/.3
3
A
.3 ~ '15-
S'.
23. csc A
=- I 3
·1-:=.. 3/r
26. csc B "- !:JIV
. ::...!j/r
24. cot A -;:. '//3
te"'- A::;
JI-J
27. cot 8 .:. 3/y
(,,- /3 ~
V(.J'
b
C