Name
~
~
Date
Period __
,..........._
WORKSHEET - TRIG RATIOS
In each of the following problems, the terminal side of an angle in standard
position passes through point P. Draw () and find the exact values of the
six trig functions of (J.
.'
Shit)
1. P(3,4)Q
==
l
5
~e.:
Lt
Sec.. e ':.§..
=~
-tan e '; :t.
t.OSS
~
~
3
~ e
3
=.a
4:f
2. P (12, -5)
D'
v \V')
9
:;
c~c..e: -'~
- f!;
5
5ec. Q -=-
tose:.~
•
r: ~ "4.
3~2,...'"
c:..t>S> ~-:-~
-3
,~
-.Rl
-:
Lecl"\_~
~__L
V£ '-'
-\-C1.~ e":
CS\ V\ e =
C"2-
...... ~__..'
CI' -
OS~-;-~
-
-t;g;.Jf:
Sec e :-:::-2:
~
L.l>~ S:-T
t5GG::. ~
~-=-J5
•
S\(\~:: -a,
;0
-6.n ~r:.- ~
3 r"' 2
~
~'=>
.lm,(\9-: -~;¥O&
-\
td
C!E:£.-e -
-
_ Cfl.CQ -=
~
\W\ ~ ~~
to
8. sec S =
~~-t:-3
_I(;'"
~
$ec.9~-JS
~
L_t
~cJ
co~e~-4
21t ~ =-~
2
to~e':.-g
c~ce~---
Si"''d-:. -~
e in
7. sinS= 2'1 1t <s<_31t
~'":\
5ec.e~ ~'""
~1-r1t< S <
6. cos S = -
5
'-oJ 1
Find the exact values of the other five trig functio~s for an angle
standard position, given the following.
5. cosO=_24~_7Z'<0<0
25 r 2
12-
~ -V'L
~
c...o\-B> - \
~~o:.
P (-2, 3)
Ii
-4"
-_
Cot e ~
-w.() G ':.-5.-SiV\& ::~-:-.A c.ste~=,~-:: :.rz;
3. P, (-3, -3)
. ..,.
.if7-
~
eo\-e-, ~~
< S < 1t
~-:-J3
CD~e": ~
.,.
~
S\ne:: &
~
,
-\-o_f\ ~ ~ ~::;;
c~c.e- ~
-~
tDt~- \
.. ~
(
Name
'"
Period
Date
pt'~
Worksheet
_
Find the reference angle for each angle.
- Coterminal, Reference, and Special Angles
13.300
Find two angles (one in a clockwise direction and the other in a counterclockwise
direction, from the given angle) that are coterminal to the following:
1.3300
-
3C), LijO
_gi, ~\OD
3.450"
5
-:1E
rut'
(p ,
(p
511"
'6
2. -750
15. 711 a=
435 ~~~5°
-
4. 35·
6.
7r
-2"
-3~5~ 2>~5°
-2lt
2-,
-if ,1f
~IO-~
~_
22. 5n-
4
23. ::!!..
3
-;. /..QD-
~Y'\ .
~14
25. -4%
3
~1t'--lJlt(p
I/.
1ft)
16. 51t
3
:: 1!
(0
~-~
3
:3
a= ~
5 rr)
to degrees or degrees to radians.
18. -1500= __
/~
"1"•
-711" 18 -__J..LL
Give a coterminal angle that
is in the given interval.
12
fl'
t,
In which quadrant does the terminal
side of each angle lie when it is in
standard position?
3
?P-Y'\
4
IP
~
20.
24. 111t
12. 6 = 11Jt
6
1!r_~
a:5!:l_
19. 51t=~D
21. 21t
\~-l20
•
14. -1500
17. 45· =~
Y
10. 6 = 120·
11. 6= 51t
ff).,
6
Draw each angle, 9, in standard position. Find the reference angle, n.
Label 9 and a.
~~
a=.M
Convert fro~adianS
~ '_~81:
7. 1311
6
~Lt-
c
(
D
11
26. 55°, [-360', OJ
-m:
27. 572°, [0', 360°)
X
~
1
305
28. -113°, [0.,360')
29
,,;1.1). "
~
"f1 0
3Str'/ .
1111"
. 12,(2",411] ~
-411"
30 .3' [0, 2lt]
~'Irl
- I~