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Odd and even Function Worksheet

Odd and even Function Worksheet
  • Page 1
 1.  
What is the period of the function y = - 1 2tan 3x?
a.
3π
b.
π6
c.
2π3
d.
π3


Solution:

y = - 1 / 2tan 3x
[y = a tan bx.]

Period is π3 or (180 / 3)°.
[πb or (180b)°.]


Correct answer : (4)
 2.  
Find the period of the function y = tan 4x.
a.
90o
b.
45o
c.
50o
d.
720o


Solution:

y = tan 4x
[y = a tan bx.]

Period is π4 or (180 / 4
[πb or (180b)°.]

= π4 or 45°


Correct answer : (2)
 3.  
Which of the following is true for the function y = cos x?
a.
Even function
b.
Odd function
c.
Odd and even function
d.
Cannot be determined


Solution:

If x is the measure of an angle with terminal side in quadrant I, then - x is the measure of an angle with terminal side in quadrant IV. Similarly, if x is the measure of a quadrant IV angle, then - x is the measure of a quadrant I angle. In either case, since cos x is negative in both quadrants I and II, cos(- x) = cos x.

If x is the measure of an angle with terminal side in quadrant II, then - x is the measure of an angle with terminal side in quadrant III. Also, if x is the measure of a quadrant III angle, then - x is the measure of a quadrant II angle. In either case, since cos x is negative in both quadrants II and III, cos(- x) = cos x.

Since cos (- x) = cos x for all values of x in the domain of the function, y = cos x is an even function.


Correct answer : (1)
 4.  
Which of the following is true for the function y = csc x?
a.
Odd function
b.
Even function
c.
Odd and even function
d.
Cannot be determined


Solution:

If x is the measure of an angle with terminal side in quadrant I, then - x is the measure of an angle with terminal side in quadrant IV. Similarly, if x is the measure of a quadrant IV angle, then - x is the measure of a quadrant I angle. In either case, since csc x is negative in quadrant IV and positive in quadrant I, csc (- x) = - csc x.

If x is the measure of an angle with terminal side in quadrant II, then - x is the measure of an angle with terminal side in quadrant III. Also, if x is the measure of a quadrant III angle, then - x is the measure of a quadrant II angle. In either case, since csc x is negative in quadrant III and positive in quadrant II, csc (- x) = - csc x.

Since csc (- x) = - csc x for all values of x in the domain of the function, y = csc x is an odd function.


Correct answer : (1)
 5.  
Find the period of the function y = 2 cot x.
a.
2π
b.
π
c.
π2
d.
2π


Solution:

y = 2 cot x
[y = a cot bx.]

Period is π1 or (180 / 1
[πb or (180b)°.]

= π or 180°


Correct answer : (2)
 6.  
Find the period of the function y = 5 3 cos (x3).
a.
60o
b.
540o
c.
300o
d.
108o


Solution:

y = 5 / 3 cos (x3)
[y = a cos bx.]

Period is π13 or (18013
[π2 or (180b),°.]

= 3π or 540°


Correct answer : (2)
 7.  
What is the period of the function y = - 3 2sec 2x ?
a.
3π
b.
π2
c.
π
d.
2π


Solution:

y = - 3 / 2sec 2x
[y = a sec bx.]

Period is 2π2 or (360 / 2)o
[2πb or (2 × 180b)o.]

= π or 180o


Correct answer : (3)
 8.  
Find the period of the function y = sec 6x + 3 2.
a.
90o
b.
60o
c.
30o
d.
216o


Solution:

y = sec 6x + 3 / 2
[y = a sec bx + c.]

Period is 2π6 or (360 / 6)o
[2πb or (360b)o.]

= π3 or 60o


Correct answer : (2)
 9.  
Find the period of the function y = 2 csc (x2).
a.
π
b.
4π
c.
π2
d.
2π


Solution:

y = 2 csc (x2)
[y = a csc bx.]

Period is 2π12 or (36012)o
[2πb or (360b)o.]

= 4π or 720o


Correct answer : (2)
 10.  
Find the period of the function y = - 3 csc (2 3)x.
a.
3π4
b.
3π
c.
3π2
d.
4π3


Solution:

y = - 3 csc (2 / 3)x
[y = a csc bx.]

Period is 2π23 or (36023
[2πb or (360b)°.]

= 3π or 540°


Correct answer : (2)

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