Chapter 6 Trig 1060. Find an equation that completes the fundamental trigonometric identity. Sin(-x)= 1.csc x 2.-sin x 3.-csc x 4.sin x.

Chapter 6Trig 1060

Find an equation that completes the

fundamental trigonometric identity. Sin(-x)=

csc

x

-sin

x

-csc

x

sin

x

0% 0%0%0%

1. csc x

2. -sin x

3. -csc x

4. sin x

Find the expression that completes the fundamental trigonometric identity.

tan

u

-tan

u

-cot

u

cot u

0% 0%0%0%

tan( )2

u1. tan u

2. -tan u

3. -cot u

4. cot u

Use trigonometric substitution to write the algebraic expression as a trigonometric function of

, . , secwhere x x02

7 28 22

* * * *

0% 0% 0%0%0%

2 7 tan4 7 sin2 7 2 cos

28 2tan

1. *

2. *

3. *

4. *

Factor the expression and use the fundamental identities to simplify

cos csc cos2 2 2x x x

* * * *

1

0% 0%0%0%

cos tan2 2x xcos2 xcos cot2 2x x

1. *

2. *

3. *

4. * 1

Use the given values to evaluate (If possible) the remaining trigonometric functions

• Sin x• Cos x• Sec x• Cot x

csc , tanx x 109

10

10

3

Find a fundamental identity that could be used to verify the identity given

Pyt

hagor

ean id

entit

y

Quot

ient i

dentit

y

Eve

n/odd

iden

tity

Cofu

nctio

n iden

tity

0% 0%0%0%

sin

cos

2

211

x

x

1. Pythagorean identity

2. Quotient identity

3. Even/odd identity

4. Cofunction identity

Find an expression to complete the identity

2 22sin cos

csc

x x

x

0% 0% 0%0%

1 sincos

x

x1. *

2. * sinx

3. *

4. * cos x

1 csccsc

x

x

Find an expression that completes the identity

-2 s

in x 0

Tan

x

2 +

cos

x

0% 0%0%0%

sin

cos

cos

sin

x

x

x

x1

1

1. -2 sin x

2. 0

3. Tan x

4. 2 + cos x

Find an expression to complete the identity

1. * 1

2. *

3. *

4. *

sin ( csc )2 21t t

* 1 * * *

0% 0%0%0%

sin4 tsin2 1t 1 2 sin t

Find the x-values that are solutions of the equation

1. *

2. *

3. *

4. *

5 15 02cot x

* * * *

0% 0%0%0%

4 2

2

3

5

6, , ,

3

2

3

4

3

5

3, , ,

4

3

4

5

4

7

4, , ,

6

5

6

7

6

11

6, , ,

Express sin9x-sin5x as a product containing only sines and/or cosines

-2si

n2xco

s7x

-2si

n7xco

s2x

2si

n7xc

os2x

2si

n2xc

os7x

0% 0%0%0%

1. -2sin2xcos7x

2. -2sin7xcos2x

3. 2sin7xcos2x

4. 2sin2xcos7x

Use the figure to find the exact value of the trigonometric function

tan2

8

6

10

3

10

1

3

1. *

2. *

3. *

4. * 3

Find the exact value of the following using the half-angle formulas

cos2

* * * *

0% 0%0%0%

10

102

5

10

10

2

5

cos ,

4

5

3

2

1. *

2. *

3. *

4. *

Use the power-reducing formulas to find the exact value of the trigonometric function

1. *

2. *

3. *

4. *

cos27

12

* * * *

0% 0%0%0%

2 3

4

2 3

4

3 2

2

3 2

2

Use the power-reducing formulas to find the exact value of the trigonometric function

sin2 135o

* * * *

0% 0%0%0%

1

2

1

2

1 2

2

1 2

2

1. *

2. *

3. *

4. *

Find the exact value of sin2x using the double angle formulasin ,x x

1

15

3

2

* * * *

0% 0%0%0%

223

225

223

225

8 14

225

8 14

225

1. *

2. *

3. *

4. *

Find the exact values of sin2x and cos2x using the double angle formulasin ,x

8

15

3

22

* * * *

0% 0%0%0%

16 161

225

97

225,

97

225

16 161

225,

97

225

16 161

225,

16 161

225

97

225,

1. *

2. *

3. *

4. *