Math Analysis Honors – Worksheet 94
Solving Trigonometric Equations
Find all solutions of the equation in the interval 0, 2  algebraically.
1. csc2 x  2  0
2. 2sin2 x  2  cos x
3. sec2 x  sec x  2
4. sec x csc x  2 csc x
5. 2sin x  csc x  0
6. sec x  tan x  1
7. cos x  sin x tan x  2
8. cos 2x 2 cos x 1  0
9. 4 sin2 x  4 cos x 1
Use a graphing calculator to graph function (a) f x  and approximate the x-coordinate of the maximum and minimum
points of the graph in the interval 0, 2  . Solve the trigonometric equation (b) in the interval 0, 2  algebraically.
Explain what you notice.
10. (a) f x   sin 2x
11. (a) f x   sin2 x  cos x
(b) 2 cos 2x  0
(b) 2sin x cos x  sin x  0
12. (a) f x   sin x  cos x
(b) cos x  sin x  0
13. (a) f x   2sin x  cos 2x
(b) 2cos x  4 sin x cos x  0
Math Analysis Honors – Worksheet 94
Solving Trigonometric Equations
Find all solutions of the equation in the interval 0, 2  algebraically.
1. csc2 x  2  0
2. 2sin2 x  2  cos x
3. sec2 x  sec x  2
4. sec x csc x  2 csc x
5. 2sin x  csc x  0
6. sec x  tan x  1
7. cos x  sin x tan x  2
8. cos 2x 2 cos x 1  0
9. 4 sin2 x  4 cos x 1
Use a graphing calculator to graph function (a) f x  and approximate the x-coordinate of the maximum and minimum
points of the graph in the interval 0, 2  . Solve the trigonometric equation (b) in the interval 0, 2  algebraically.
Explain what you notice.
10. (a) f x   sin 2x
11. (a) f x   sin2 x  cos x
(b) 2 cos 2x  0
(b) 2sin x cos x  sin x  0
12. (a) f x   sin x  cos x
(b) cos x  sin x  0
13. (a) f x   2sin x  cos 2x
(b) 2cos x  4 sin x cos x  0