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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