ADAMSON UNIVERSITY
Mathematics Department
PLANE & SPHERICAL TRIGONOMETRY- Long Quiz no.4 1st Sem. S.Y.2012-2013
GENERAL DIRECTION:
A. Write the EXAM CODE at the UPPER RIGHT CORNER of your ANSWER SHEET.
B. For items 1-15, choose the letter of the correct answer. Write the letter of your choice on the answer sheet.
C. DO NOT WRITE ANYTHING ON THIS QUESTIONNAIRE.
======================================================================================
Solve the problem.
x 2 , does the
6) For what numbers x, -2
graph of y = csc x have vertical asymptotes?
1) What is the range of the cotangent function?
3
3
A) all real numbers, except integral
,- , ,
A) 2
2 2 2
multiples of (180)°
B) all real numbers from -1 to 1, inclusive
B) -2 , - , 0, , 2
C) all real numbers greater than or equal to
1 or less than or equal to -1
C) -2, -1, 0, 1, 2
D) none
D) all real numbers
2) What is the range of the secant function?
A) all real numbers
B) all real numbers greater than or equal to
1 or less than or equal to -1
C) all real numbers from -1 to 1, inclusive
7) A rotating beacon is located 6 ft from a wall. If
the distance from the beacon to the point on the
wall where the beacon is aimed is given by
a = 6|sec 2 t|,
where t is in seconds, find a when t = 0.35
seconds. Round your answer to the nearest
hundredth.
D) all real numbers, except odd multiples of
2
(90)°
B) 27 + 3
C) 27
D) undefined
not defined?
A) all real numbers
B) odd multiples of
D) odd multiples of
2
D) 13.22 ft
C) -
2
x
2 , does
B) -2 , 0, 2
,
3
2
D) none
x 2 , does the
9) For what numbers x, -2
graph of y = tan x have vertical asymptotes.?
(180°)
C) integral multiples of
C) 10.21 ft
A) - ,
A) 29
is f( ) = cot
B) 11.71 ft
8) For what numbers x, -2
csc x = -1?
3) If cot = 9.0, find the value of
cot + cot ( + ) + cot ( + 2 ).
4) For what numbers
A) -10.21 ft
A) -2 , - , 0, , 2
(180°)
B) -2, -1, 0, 1, 2
3
3
,- , ,
C) 2
2 2 2
(90°)
D) none
x 2 , does the
5) For what numbers x, -2
graph of y = tan x have vertical asymptotes.?
A) -2, -1, 0, 1, 2
3
3
,- , ,
B) 2
2 2 2
10) Find the general equation of the asymptote of
the function: y= 3 csc (3x -
A) x=
C) -2 , - , 0, , 2
B) x=
D) none
C) x=
D) x=
simon.ogbac PST long quiz no.4
1 SET A
3
6
3
6
(k+1), k Z
(3k+2), k Z
(k+1), k Z
(2k+1), k Z
2
)+1
14) Find the equation of the function of the form:
y = a sec bx + d
1
1
A) y= sec(4x)
B) y = sec(2x)
2
2
11) Find the equation of the function of the form:
y = a tan (bx) + d in the given graph below.
1
1
C) y= sec(2x)4
2
D) y=sec(4x)-
1
2
15) At what value of x is the function undefined?
A) 0
B)
C)
D)
4
8
2
PART II. Sketch 1 cyle of the graph of the given
function below. Determine the following:
A) y= tan(3x)- 1
B) y = 2tan(6x)+1
C) y=2tan(3x)+1
D) y = 2 tan (3x)+1
a. Period
b. Phase shift
c. Vertical shift
d. General equation of the asymptote
e. Domain
f. Range
FOR ITEMS 12-13, REFER TO THE GIVEN
GRAPH BELOW.
y = 3 tan (2x -
12) What is the range of the function?
A) (
,1]
[3,
C) [1, 3]
)
B) y 2k, k Z
D) (
,+ )
13) Find the period of the function.
A) 1
B) 4
C) 3
D) 2
FOR ITEMS 14-15, REFER TO THE GIVEN
GRAPH BELOW.
simon.ogbac long quiz no.4
2
SET A
4
)