Exam 1
1.
Write equation of the circle centered at (3, -10) and
passing through (-1,-6)
r
2
=
(
x
−
h
)
2
+
(
y
−
k
)
2
r
2
=
[
3
−
(
1
−
1
)
]
2
+
[
−
10
−
(
−
6
)
]
2
r
2
=
4
2
+(−
4
)
2
r
2
=
16
+
16
=
32
Ans
:
(
x
−
3
)
2
+
(
y
+
10
)
2
=
32
2.At what point of the first quadrant does the line with equation y=x+2 intersect the circle with radius 6 and center (0,2)?
3.
On a circle of radius 5 miles, find the length of an arc
that subtends a central angle of 3 radius.
5
(
3
)
=
15
mi
4.
A sector of a circle has a central angle of 45 degrees.
Find the area of the sector if the radius of the circle is 9
cm.
π
(
r
)
2
×
45
°
360
°
π
(
9
)
2
×
45
360
Ans
:31.8086
c m
2
5.
For an angle of
5
π
3
radians, give the reference
angle and which quadrant the angle lies in. Then compute
the sine and cosine of the angle.
5
π
3
×
180
π
=
300
°
=
4
th quadrant
360
°
−
300
°
=
60
°
=
π
3
sin
(
300
°
)=
−
√
3
2
cos
(
300
°
)=
1
2
6.
Give an angle
with
0
°
<
θ
<
360
°
that has the
same sine value as 70
°
. (answer cannot be 70
°
)
110
°
180
°
−
70
°
=
110
°
7.
Find the exact value of the 6 trig functions for an angle of
3
π
4
3
π
4
=
3
π
4
×
180
π
=
135
°
180
°
−
135
°
=
45
°
sin
(
135
°
)
=
√
2
2
,csc
(
135
°
)
=
√
2
cos
(
135
°
)
=
−
√
2
2
,sec
(
135
°
)
=
2
−
√
2
tan
(
135
°
)
=−
1,cot
(
135
°
)
=−
1
8.
Prove the identity:
csc
2
x
−
sin
2
x
cscx
+
sinx
=
cosxcotx
csc
2
x
−
sin
2
x
cscx
+
sinx
=
(
cscx
+
sinx
) (
cscx
−
sinx
)
cscx
+
sinx
=
1
sinx
−
sinx
1
(
sinx
sinx
)
=
(
1
−
sinx
sinx
)
=
cos
2
x
sinx
cosxcotx
=
cosx
(
cosx
sinx
)
=
cos
2
x
sinx
9.
In a right triangle with legs a=6ft and b=8ft, and angle A
opposite side a, fine the 6 trig functions of angle A.
r
2
=
6
2
+
8
2
r
=
10

sin
=
6
10
=
3
5
,csc
=
5
3
a=6
c=10
cos
=
8
10
=
4
5
,sec
=
5
4
tan
=
6
8
=
3
4
,
cot
=
4
3
b=8
10.A 40-ft ladder leans against a building so that the angle between the ground and the ladder is 80 degrees. How high does the ladder reach up the side of the building?

1.
Sketch one period of f(x)=-2cos(2x)+1 and label 5 key
points(beginning and ending of one period, halfway
across the period, and ¼ and ¾ of the way across the
period)
Amp: 2 ; per:
2
π
2
=
π
vertical shirt: 1 up
range 2[-1,1] +1 = [-1,2]+1 =[-1,3]
Mid line:y=1
3
2
1
y=1
-1
2.
For the function
y
=
4sin 3
(
x
−
π
6
)
−
5
, give
the amplitude, period, horizontal shift, and midline.

#### You've reached the end of your free preview.

Want to read all 11 pages?

- Fall '13
- SimonRubinstein-Salzedo
- Trigonometry, sinθ