math home work with show work i need it in 13 hours

Math 1720 Section 003 (2014S) (HW 7.4A) Date: __________________________________

Name__________________________ Class ID:________________________________

Please write neatly and show all work.

1. Fill blanks:

)sin()sin()cos()cos()cos( βαβαβα −=+ )sin()sin()cos()cos()cos( βαβαβα +=−

)cos()sin()cos()sin()sin( αββαβα +=+ )cos()sin()cos()sin()sin( αββαβα −=−

___________)cos()sin()cos()sin()sin()2sin( =+=+= ααααααα

______________________________)sin()sin()cos()cos()cos()2cos( ===−=+= ααααααα

( )_______ tan2

)tan( )2cos(

)2sin( )2tan(

α αα

α

α α =+==

, 2

2cos1 (?))cos(

α α

+ ±= ,

2

2cos1 (?))sin(

α α

− ±=

α

α

α

α α

2cos1

2cos1 (?)

)cos(

)sin( )tan(

+

− ±==

, 2

cos1 (?))

2 cos(

αα + ±= ,

2

cos1 (?))

2 sin(

αα − ±=

α

α α

α α

cos1

cos1 (?)

) 2

cos(

) 2

sin(

) 2

tan( +

− ±==

( )______ cos1

cos1

sin

) 2

cos(

) 2

sin(

) 2

tan( α

α

α α

α α −

= +

==

2. Give product to sum identities.

3. Given that cos α = 5

3 , and sin α <0 find:

sinα cosα tanα cotα secα cscα α @ Quadrant

sin 2α cos 2α tan 2α cot 2α sec 2α csc 2α 2α @

Quadrant

sin(α/2) cos(α/2) tan(α/2) cot(α/2) sec(α/2) csc(α/2) (α/2) @

Quadrant

4. Given that cos α = 3

2 , and πα

π 2

2

3 << find:

5. Given that cos 2α = 5

4 , and °<<° 18090 α find:

sin α cos α tan α cot α sec α csc α α @ Quadrant

sin (2α) cos (2α) tan (2α) cot (2α) sec (2α) csc (2α) 2α @

Quadrant

sin(α/2) cos(α/2) tan(α/2) cot(α/2) sec(α/2) csc(α/2) (α/2) @

Quadrant

sin 2α cos 2α tan 2α cot 2α sec 2α csc 2α 2α @

Quadrant

sin (4α) cos (4α) tan (4α) cot 4α) sec (4α) csc (4α) 4α @

Quadrant

sinα cosα tanα cotα secα cscα α @ Quadrant