Precalculus Chapter 5 Quiz – 40 Points Name Solve the following

Precalculus Chapter 5 Quiz – 40 Points
Name ____________________________
Solve the following equations on [0,360°) . No calculators allowed. (1-6 = 4 pts, 7,8 = 6 pts).
"2sin x "1 = 0
2sin x = "1
1)
cos2 x = cos x
cos2 x " cos x = 0
!
2) cos x (cos x "1) = 0
"1
2
x = 210°,330°
sin x =
cos x = 0
cos x = 1
x = 90°,270°, x = 0°
!
!
3)
2cos2 x = 1
1
cos2 x =
2
2sin 2 x = 3 sin x
2sin 2 x " 3 sin x = 0
(
sin x 2sin x " 3
4)
2
2
x = 45°,135°,225°,315°
cos x = ±
sin x = 0
)
2sin x = 3
3
2
x = 0°,180°,60°,120°
sin x =
!
2cos2 x + 3cos x + 1 = 0
!
sin 2 x " sin x = 2
(2cos x + 1)(cos x + 1) = 0
sin 2 x " sin x " 2 = 0
cos x = "1
5) 2cos x = "1
"1
cos x =
2
x = 120°,240°,180°
6) (sin x + 1)(sin x " 2) = 0
sin x = "1
x = 270°
sin x = 2
No solution
!
!
cos x + 1 = "sin x
2
(cos x + 1) = ("sin x )
cos2x " sin 2x + 1 = 0
2
2cos2 x "1" 2sin x cos x + 1 = 0
cos2 x + 2cos x + 1 = sin 2 x
2cos2 x " 2sin x cos x = 0
cos2 x + 2cos x + 1 = 1" cos2 x
2cos x (cos x " sin x ) = 0
2
7) 2cos x + 2cos x = 0
8) cos x = 0
2cos x (cos x + 1) = 0
cos x = 0
cos x = "1
x = 90°,270°
x = 180°
x = 90°,270°
90° is not a solution
!
!
cos x = sin x
sin x
1=
cos x
tan x = 1
x = 45°,225°