trigonometry questions

Question

1. Sketch the following graphs for the given domain.
2. y = sin x                    0 ≤ x ≤ 4 π
3. y = tan 2x                   – 180° ≤ x ≤ 180°
4. y = 2 cos 2x + 1             0 ≤ x ≤ 2 π
5. Solve the following equations for the given domain.
6. tan x = 1.9                  0° ≤ x ≤ 360°
7. sin 2x – 3 = –2.4             0° ≤ x ≤ 360°
8. 5 cos 12 x = 0.5              0 ≤ x ≤ 2 π
9. cos (2x + π) = –0.2           0 ≤ x ≤ 2 π
10. Solve the following for the given domain.
11. sin 2x = cos x                0 ≤ x ≤ 2π
12. 4 tan x1 – tan2 x = 1               0 ≤ x ≤ 2 π
13. cos 2x + 2 cos2 x = –3 cos x    0° ≤ x ≤ 360°
14. 2 cos2 x + sin x – 1 = 0        0° ≤ x ≤ 360°

Answer 1

1. Sketch the following graphs for the given domain.
2. y = sin x                    0 ≤ x ≤ 4 π
3. y = tan 2x                   – 180° ≤ x ≤ 180°
4. y = 2 cos 2x + 1             0 ≤ x ≤ 2 π
5. SORRY CAN'T SKETCH THESE. USE A CALCULATOR TO PLOT THEM
6. The following solutions comprise identities to simplify and solve. All the details are not shown or you
7. can just plot them for a solution.
8. Solve the following equations for the given domain.
9. tan x = 1.9                  0° ≤ x ≤ 360° x = 62,2°
10. sin 2x – 3 = –2.4             0° ≤ x ≤ 360° Sin 2x = 0.6 x = 15.48°
11. 5 cos 12 x = 0.5              0 ≤ x ≤ 2 π Cos 12x = 0.1 x = 84.26°
12. cos (2x + π) = –0.2           0 ≤ x ≤ 2 π 2x+π = 101.54° x = -39.23°
13. Solve the following for the given domain.
14. sin 2x = cos x                0 ≤ x ≤ 2π Sin 2x = 2SinxCosx = Cosx, Sinx = 1/2 x = 30° or π/6
15. 4 tan x1 – tan2 x = 1      0 ≤ x ≤ 2 π 4(Tanx) - (Tanx)^2 = 1 Solve by Tanx = Sinx/Cosx.....
16. x = 15°
17. c. cos 2x + 2 cos2 x = –3 cos x    0° ≤ x ≤ 360° Simplify using Cos2x=2(Cosx)^2 - 1,
18. x = 75.5° and 180°
19. d. 2 cos2 x + sin x – 1 = 0        0° ≤ x ≤ 360°
20. Simplify using Cos(x)^2 = 1= Sin(x)^2 x = π/2 and -π/6