Download Questions for Sections 7.6

Dammam Community College
MATH 012
Past Exam Questions
Section 7.6
1. If 0  x  2 , then the sum of all solutions of the equation 2 cos 2 x  cos x  1  0 is equal to
Answer: 3


2. If 0  x  2 , then the number of all solutions of the equation 2sin  2 x    1  0 is
6

Answer: 4
3. Find the exact solutions, in radians, of the trigonometric equation 3sin x  2 cos 2 x  0 .

5
 2 k . where k is an integer.
Answer: x   2 k ,
6
6
4. Find the exact solutions of the trigonometric equation sin
x
 cos x  1, 0  x  360.
2
Answer: x  0 , 60 , 300.
 3 
5. The sum of the solutions of 2sin x cos x  3 cos x  2sin x  3  0 in the interval  0,
 is
2 

7
Answer:
3
2 
3

6. The number of solutions of the equation cos  2 x 
 0 in the interval  0, 2  is

3  2

Answer: 4
7. Solve the trigonometric equation 2sin 2 x  3sin x  1  0 , where 0  x  2 .
7 11 3
,
,
Answer: x 
6 6 2
1
With regards of Dr. Ali Al-Karkhy
Dammam Community College
MATH 012
8. Find all values of x for which sec 2 x  1  tan 2 2 x.
Answer: x  k , where k is an integer.
9. Solve the trigonometric equation cos x  cos 2
Answer: x 
x
3
  , where 0  x  2 .
2
4
2 4
,
3 3
10. Find the set of solutions of the trigonometric equation sin 3 x  1, give your answer in terms of  and n,
where n is an integer number.

Answer: x  (1  4n)
6

x 

11. Find the set of solutions of the trigonometric equation tan     1  cos  x   , where 0  x  2 .
3
2 6

(Hint: you may use the half-angle Identities, also be careful of any extraneous solution).
  5 
Answer: solution set   , 
6 3 
2
With regards of Dr. Ali Al-Karkhy