Trigonometry 6.5 short version

6.5 Trigonometry short version Name___________________________________

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Use substitution to determine whether the given x-value is a solution of the equation.

1) sin x = - 3 , x = 4!

1)

2

3

2) tan x = 3 , x = 7!

2)

3

6

3) sin x = - 2 3 , x = -2!

3)

3

3

4) cos 2x = - 2, x = 3!

4)

4

5) cos x + 1 = sin x, x = -3!

5)

4

Find all solutions of the equation.

6) cos x = 0

6)

7) 2 cos x - 3 = 0

7)

8) 8 cos x - 6 3 = 6 cos x- 5 3

8)

Solve the equation on the interval [0, 2!).

9) cos 2x = 2

9)

2

10) sin 4x = 3

10)

2

Find all solutions of the equation.

11) tan x sec x = -2 tan x

11)

Solve the equation on the interval [0, 2!).

12) cos x = sin x

12)

13) sin2 x - cos2 x = 0

13)

1

14) sin2 x + sin x = 0

14)

Solve the equation on the interval [0, 2!).

15) (tan x - 1) (cos x + 1) = 0

15)

16) cos x + 2 cos x sin x = 0

16)

Solve the equation on the interval [0, 2!).

17) tan 2x - tan x = 0

17)

18) sin2 2x = 1

18)

19) cos 2x = 2 - cos 2x

19)

20)

cos

x

+

! 3

+ cos

x

-

! 3

= 1

20)

Determine the specific solutions (if any) to the equation on the interval [0, 2!).

21) sec2" - 2 = tan2 "

21)

22) 2 cos2" + sin " - 2 = 0

22)

23) cot2 " cos " = cot2 "

23)

24) sin " + 2 sin " cos " = 0

24)

2

Answer Key Testname: TRIGONOMETRY 6.5 SHORT VERSION

1) Yes 2) Yes 3) No 4) No 5) No 6) ! + n!

2

7)

x

=

! 6

+ 2n!

or

x

=

11! 6

+ 2n!

8)

x

=

! 6

+ 2n!

or

x

=

11! 6

+ 2n!

9)

!, 8

7! , 8

9! , 8

15! 8

10)

!, 12

!, 6

2! , 3

7! , 12

7! , 6

13! , 12

5! , 3

19! 12

11)

x

=

2! 3

+ 2n!

or

x

=

4! 3

+ 2n!

or

x

=

n!

12)

!, 4

5! 4

13)

!, 4

3! , 4

5! , 4

7! 4

14) 0, !, 3! 2

15)

! 4

,

!,

5! 4

16)

! 2

,

7! 6

,

3! 2

,

11! 6

17) 0, !

18)

!, 4

3! , 4

5! , 4

7! 4

19)

!, 8

7! , 8

9! , 8

15! 8

20) 0 21) no solution 22) 0, !, ! , 5!

66

23)

!, 2

3! 2

24)

0,

2 3

,

!,

4 3

3

 ................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download