Regents Exam Questions Name: ________________________
F.TF.A.2: Determining Trigonometric Functions 4
www.jmap.org
1
F.TF.A.2: Determining Trigonometric Functions 4
1 If
is an angle in standard position and
P(3, 4)
is
a point on the terminal side of
, what is the value
of
sin
?
1)
3
5
2)
3
5
3)
4
5
4)
4
5
2 If the terminal side of angle
q
, in standard position,
passes through point
(4,3)
, what is the numerical
value of
sin
?
1)
3
5
2)
4
5
3)
3
5
4)
4
5
3 If the terminal side of angle
passes through point
(4,3)
, what is the value of
cos
?
1)
3
5
2)
3
5
3)
4
5
4)
4
5
4 A circle centered at the origin has a radius of 10
units. The terminal side of an angle,
, intercepts
the circle in Quadrant II at point C. The
y-coordinate of point C is 8. What is the value of
cos
?
1)
3
5
2)
3
4
3)
3
5
4)
4
5
5 Circle O has a radius of 2 units. An angle with a
measure of
6
radians is in standard position. If the
terminal side of the angle intersects the circle at
point B, what are the coordinates of B?
1)
3
2
,
1
2
Ê
Ë
Á
Á
Á
Á
Á
Á
Á
Á
Á
ˆ
¯
˜
˜
˜
˜
˜
˜
˜
˜
˜
2)
3,1
Ê
Ë
Á
Á
Á
ˆ
¯
˜
˜
˜
3)
1
2
,
3
2
Ê
Ë
Á
Á
Á
Á
Á
Á
Á
Á
Á
ˆ
¯
˜
˜
˜
˜
˜
˜
˜
˜
˜
4)
1, 3
Ê
Ë
Á
Á
Á
ˆ
¯
˜
˜
˜
Regents Exam Questions Name: ________________________
F.TF.A.2: Determining Trigonometric Functions 4
www.jmap.org
2
6 If
is an angle in standard position whose terminal
side passes through the point
(2,3)
, what is the
numerical value of
tan
?
1)
2
3
2)
3
2
3)
2
13
4)
3
13
7 Angle
is in standard position and
(4,0)
is a point
on the terminal side of
. What is the value of
sec
?
1)
4
2)
1
3) 0
4) undefined
8 If the terminal side of angle
passes through point
(3,4)
, what is the value of
sec
?
1)
5
3
2)
5
3
3)
5
4
4)
5
4
9 If
is an angle in standard position whose terminal
side passes through the point
(3,4)
, which
statement is true?
1)
sec
0a
n
d
t
a
n
0
2)
sec
0a
n
d
t
a
n
0
3)
sec
0a
n
d
t
a
n
0
4)
sec
0a
n
d
t
a
n
0
10 The origin of a coordinate grid is labeled A. Line
segment AB forms an angle of 30° with the x-axis.
If
AB 8
, the coordinates of B are:
1)
(6,4)
2)
(8cos 30,8s
n
30)
3)
(8s
n
30,8cos30)
4)
(4,4 3)
11 An angle,
, is in standard position and its terminal
side passes through the point
(2,1)
. Find the exact
value of
sin
.
12 If
is an angle in standard position and its terminal
side passes through the point
(3,2)
, find the exact
value of
csc
.
13 Determine the exact value of
csc
P
if P is an angle
in standard position and its terminal side passes
through the point
(5,8)
.
ID: A
1
F.TF.A.2: Determining Trigonometric Functions 4
Answer Section
1 ANS: 3
sin
y
x
2
y
2
4
(3)
2
4
2
4
5
REF: 010616b
2 ANS: 1
A reference triangle can be sketched using the coordinates
(4,3)
in the second quadrant to find the value of
sin
.
REF: spr1503aii
3 ANS: 4
cos
x
x
2
y
2
4
(4)
2
3
2

4
5
REF: 068628siii
4 ANS: 1
REF: 061617aii
5 ANS: 2
x 2
3
2
3
y
2
1
2
1
REF: 061525a2
6 ANS: 2
(2)
2
(3)
2
13
;
tan
sin
cos
3
13
2
13
3
2
REF: 062304aii
ID: A
2
7 ANS: 2
sec
x
2
y
2
x
(4)
2
0
2
4
4
4
1
REF: 011520a2
8 ANS: 2
cos

3
5
sec

5
3
REF: 011621a2
9 ANS: 4
Since the terminal side of
passes through
(3,4)
,
cos
0and sin
0
.
cos
0 sec
0
tan
sin
cos

REF: 082420aii
10 ANS: 2 REF: fall9920b
11 ANS:
1
2
2
(1)
2

1
5
REF: 061832aii
12 ANS:
13
2
.
sin
y
x
2
y
2
2
(3)
2
2
2
2
13
.
csc
13
2
.
REF: fall0933a2
13 ANS:
sinP
y
x
2
y
2
8
5
2
(8)
2
8
89
cscP 
89
8
REF: 081634a2