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2. Basic Trigonometric Functions - 8 - www.mastermathmentor.com - Stu Schwartz
Unit 2 - The Trigonometric Functions - Homework
1. Let P be a point on the terminal side of
!
" . Draw a picture showing the reference angle and find the 6 trig
functions of
!
" .
a)
!
P 12,9( ) b)
!
P 30,16( )
!
sin" =3
5 csc" =
5
3
cos" =4
5 sec" =
5
4
tan" =3
4 cot" =
4
3
!
sin" =8
17 csc" =
17
8
cos" =15
17 sec" =
17
15
tan" =8
15 cot" =
15
8
c)
!
P 1,2( ) d)
!
P 3, 7( )
!
sin" =2
5
csc" =5
2
cos" =1
5
sec" =5
1
tan" =2
1 cot" =
1
2
!
sin" =7
4 csc" =
4
7
cos" =3
4 sec" =
4
3
tan" =7
3 cot" =
3
7
e)
!
P "8,"6( ) f)
!
P 1,"3( )
!
sin" = #3
5 csc" = #
5
3
cos" = #4
5 sec" = #
5
4
tan" =3
4 cot" =
4
3
!
sin" = #3
10
csc" = #10
3
cos" =1
10
sec" =10
1
tan" =#3
1 cot" =
#1
3
g)
!
P 6," 13( ) h)
!
P " 2," 2( )
!
sin" = #13
7 csc" = #
7
13
cos" =6
7 sec" =
7
6
tan" =# 13
6 cot" =
#6
13
!
sin" = #2
2 csc" = #
1
2
cos" = #2
2 sec" = #
1
2
tan" =1 cot" =1
2. Given information about one trig function, find other trig functions:
a)
!
If tan" =4
3," in quadrant I, find cos" and sin". b)
!
If cos" =3
2," in quadrant IV, find sin" and tan".
!
sin" =4
5,cos" =
3
5
!
sin" =#1
2, tan" = #
3
3
2. Basic Trigonometric Functions - 9 - www.mastermathmentor.com - Stu Schwartz
c)
!
If sin" =5
8," in quadrant II, find sec" and cot". d)
!
If sec" = #5
2," in quadrant III, find sin" and tan".
!
sec" =#8
39,cot" =
# 39
5
!
sin" =# 21
5, tan" =
21
2
e)
!
If tan" = #5," in quadrant IV, find sin" and sec". f)
!
If cos" =2
3 and sin" < 0, find sin" and tan".
!
sin" =#5
26,sec" = 26
!
sin" =# 7
3, tan" = #
7
2
g)
!
If sec" =6
5, find sin" and tan". h)
!
If tan" =4 5
5, find sin" and cos".
!
sin" =± 11
6, tan" =
± 11
5
!
sin" =±4
21,cos" =
±5
105 or ±
5
21
3. In what quadrant is
a)
!
sin" > 0 and cos" < 0 b)
!
csc" > 0 and cot" < 0
!
II
!
II
c)
!
sec" < 0 and tan" < 0 d)
!
csc" < 0 and cos" < 0
!
II
!
III
4. Find the value of the following (do not look at the chart – make a small picture and calculate the values)
a)
!
5sin90°" 7cos180°
5 1( ) " 7 "1( ) =12 b)
!
4sec0° + 7csc270°
4 1( ) + 7 "1( ) = "3
c)
!
sin2180° + cos
2180°
0( )2
+ "1( )2
=1 d)
!
6cot3"
2+ 3sec"
#
$ %
&
' (
3
6cot 0 + 3sec )1( )( )3
= )27
e)
!
cos0°sin270°" cos270°sin0°
1 "1( ) " 0( ) 0( ) = "1 f)
!
sin270°" sec0°( ) sin270° + sec0°( )"1"1( ) "1+1( ) = 0
2. Basic Trigonometric Functions - 10 - www.mastermathmentor.com - Stu Schwartz
5. For each statement, determine whether or not it is Possible (P) or Impossible (I).
a)
!
sin" = #5 Impossible b)
!
tan" +1= 3.79 Possible
c)
!
2cos" + 5.5 = 4 Possible d)
!
sin" + cot# = 8 Possible
e)
!
csc" + sin# = .5 Possible f)
!
sin" + cos# = 2 Possible
6. Find the value of the following (do not look at the chart – make a small picture and calculate the values)
a)
!
6sin30°" 4cos150°
61
2
#
$ % &
' ( " 4
" 3
2
#
$ %
&
' ( = 3+ 2 3
b)
!
8sin60°" 4sin300°
83
2
#
$ %
&
' ( " 4
" 3
2
#
$ %
&
' ( = 6 3
c)
!
4 tan120°( ) 8cos225°( )
4 " 3( ) 8( ) "2
2
#
$ %
&
' ( =16 6
d)
!
6sin315° + 8tan135°
6 "2
2
#
$ %
&
' ( + 8 "1( ) = "3 2 " 8
e)
!
8csc 30°
cot 330°
8 2( )" 3
="16
3 or
"16 3
3
f)
!
"2cos225°" 4cot 315° + 3
"2" 2
2
#
$ %
&
' ( " 4 "1( ) + 3 = 7 + 2
g)
!
sin2225°" cos2 225°
"2
2
#
$ %
&
' (
2
" "2
2
#
$ %
&
' (
2
= 0 h)
!
cos3630°" csc3 "30°( )
0 " "2( )3
= 8
i)
!
sin"
6# 4cos
2"
3
$
% &
'
( ) 2
1
2# 4
#1
2
$
% &
'
( )
*
+ ,
-
. /
2
=25
4
j)
!
cos2 3"
4# csc2
7"
6
$
% &
'
( ) 4
#2
2
$
% &
'
( )
2
# #2( )2
*
+
, ,
-
.
/ /
4
=#7
2
$
% &
'
( ) 4
=2401
16=150.063
7. For each value of
!
" , determine the co-terminal angle and the signs of the trig functions of that angle.
!
" Co-terminal
angle
(between
!
0° and 360°)
!
sin"
!
cos"
!
tan"
!
csc"
!
sec"
!
cot"
!
700°
!
340° - + - - + -
!
1525°
!
85° + + + + + +
!
"485°
!
235° - - + - - +
!
2.5"
!
"
2
1 0 " 1 " 0
!
"20#
7
!
8"
7
- - + - - +